The Role of Pastoralist Mobility in Foot-And-Mouth Disease Transmission in the Far North Region of Cameroon

The Role of Pastoralist Mobility in Foot-and-Mouth Disease Transmission in The Far North Region of Cameroon

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Hyeyoung Kim

Graduate Program in Geography

The Ohio State University

2016

Dissertation Committee:

Ningchuan Xiao, Advisor

Rebecca Garabed

Mark Moritz

Daniel Z. Sui

Copyrighted by

Hyeyoung Kim

2016

Abstract

Animal and human movements can impact the transmission of infectious diseases. Recent outbreaks of infectious diseases such as Ebola Virus Disease, Middle Eastern Respiratory

Syndrome, Severe Acute Respiratory Syndrome, or foot-and-mouth disease (FMD) occur across borders and concurrently in the world. Because the movements of individuals and goods occur globally and frequently, an infectious disease outbreak in one place can be spread throughout the world. Therefore, analyzing and predicting movements is closely related to predicting and preventing the spread of an epidemic. Analyzing historical epidemic data and modeling the spread of an epidemic allow us to prepare for new epidemics in the near future and can also be the basis of a policy decision. Modeling animal and human movements and their impacts, however, presents a significant challenge to disease transmission models because these models often assume a fully mixing population where individuals have an equal chance to contact each other. In reality, movements result in populations that can be best represented as dynamic networks whose structure changes over time as individual movements result in changing distances between individuals within a population. This dissertation models the impact of the movements of mobile pastoralists on FMD transmission in a transhumance system in the Far North Region of Cameroon. I first analyze transhumance survey data to derive mobility rules that can be used to simulate the movements of the agents in the model. I develop an agent-based model coupled with an epidemic model. With the model, I ii simulate under the different environments and various experiment scenarios to evaluate the impacts of mobile pastoralists’ regular movements and changes in the movement patterns on hypothetical FMD epidemics. My simulation results are validated with empirical data collected by surveying herders over the last four years (2010-2014).

iii

Acknowledgments

I would like to acknowledge and express my sincerest gratitude to my committee members, colleagues, family, and friends. Without their support and encouragement, I would never have been able to endure the difficulties of the last five years.

First and foremost, I would like to express my deepest appreciation to my advisor, Dr.

Ningchuan Xiao. His wise counsel and warm encouragement have made me believe in myself and let me move forward.

I would also like to thank my dissertation committee, Dr. Rebecca Garabed, Dr. Mark

Moritz, and Dr. Daniel Sui, for their thoughtful comments, suggestions, and support toward the completion of my dissertation research.

In addition, I am grateful for productive discussions and helpful comments from the members of the Disease Ecology and Computer Modeling Laboratory (DECML) at Ohio

State. Especially, I would like to give a special thank you to Dr. Laura W. Pomeroy and

Dr. Karla Moreno Torres.

Finally, I would like to acknowledge with gratitude the support and love of my family – my parents, sister, brother-in-law, and niece.

Vita

2006...... B.Eng. Geoinformatics, University of Seoul,

South Korea

2008...... M.Eng. Geoinformatics, University of

Seoul, South Korea

2011...... Graduate Associate, Department of

Geoinformatics, University of Seoul, South

Korea

2011 to present ...... Graduate Associate, Department of

Geography, The Ohio State University, USA

Publications

Kim, H., Xiao, N., Moritz, M., Garabed, R., & Pomeroy, L. W. (2016). Simulating the Transmission of Foot-And- Mouth Disease Among Mobile Herds in the Far. Journal of Artificial Societies and Social Simulation, 19(2).

Pomeroy, L. W., Bj, O. N., Kim, H., Jumbo, S. D., Abdoulkadiri, S., & Garabed, R. (2015). Serotype-Specific Transmission and Waning Immunity of Endemic Foot- and-Mouth Disease Virus in Cameroon. PLoS ONE, 10(9), 1–16.

Jun, C., & Kim, H. (2011). A 3D Indoor Pedestrian Simulator Using an Enhanced Floor Field Model. In J. Filipe, A. Fred, & B. Sharp (Eds.), Agents and Artificial Intelligence. Springer Berlin Heidelberg, 2010. 133-146.

Jun, C., & Kim, H. (2009). An Indoor Crowd Simulation Using a 2D-3D Hybrid Data Model. In O. Gervasi, D. Taniar, B. Murgante, A. Laganà, Y. Mun, & M. L. Gavrilova (Eds.), Computational Science and Its Applications - ICCSA 2009. Springer Berlin Heidelberg, 397-412.

Kim, G., H. Kim and C. Jun, 2008. Developing a 3D indoor evacuation simulator using a spatial DBMS, Journal of Korean Society for Geospatial Information System, 16(4): 41-48. (in Korean)

Youn, G., H. Kim and C. Jun, 2008. The Optimization of Vector Data for Mobile GIS, Journal of GIS Association of Korea, 16(2): 207-218. (in Korean)

Kim, H., G. Jun and J.H. Kwon, 2007. Syntax-based Accessibility for 3D Indoor Spaces, Journal of Korean Society for Geospatial Information System, 15(3): 11-18. (in Korean)

Fields of Study

Major Field: Geography

Table of Contents

Abstract ...... ii

Acknowledgments...... iv

Vita ...... v

List of Tables ...... xi

List of Figures ...... xii

Chapter 1: Introduction ...... 1

1.1 Problem context ...... 1

1.2 Research Objectives ...... 3

1.3 Dissertation Overview ...... 3

Chapter 2: Literature Review ...... 5

2.1 Human/Animal Mobility Pattern Analysis ...... 5

2.2 Modeling Human Behavior ...... 12

2.3 Modeling Epidemic Process ...... 16

2.4 Agent-based Modeling ...... 21

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2.5 Foot-and-Mouth Disease ...... 23

Chapter 3: Simulating the Transmission of Foot-and-mouth Disease among Mobile

Herds in the Far North Region, Cameroon ...... 27

3.1 Introduction ...... 27

3.2 Data and Methods ...... 31

3.2.1 Spatial and Temporal Movements of Pastoralists ...... 31

3.2.2 Agent-Based Disease Model ...... 39

3.3 Experiments ...... 44

3.4 Results ...... 48

3.4.1 Sensitivity to parameters ...... 48

3.4.2 Model compared to survey data ...... 53

3.5 Discussion and Conclusions ...... 58

Chapter 4: Describing and Explaining Patterns in Transhumance Orbits: Pastoral

Mobility in the Far North Region of Cameroon ...... 60

4.1 Introduction ...... 60

4.2 Study Area and Data ...... 62

4.3 Methods ...... 64

4.4 Results ...... 68

4.4.1 Transhumance orbits ...... 68

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4.4.2 Migratory drift ...... 73

4.5 Discussion ...... 74

4.6 Conclusion ...... 76

Chapter 5: Modeling the effects of Transhumance Movement on the Transmission of

Foot-and-mouth Disease ...... 77

5.1 Introduction ...... 77

5.2 Background information on study area ...... 78

5.3 Design of agent-based model ...... 80

5.3.1 Landscape ...... 81

5.3.2 Agents ...... 82

5.3.3 Mobility rules ...... 83

5.3.4 Epidemic rules ...... 85

5.3.5 Model parameters ...... 87

5.4 Experiments ...... 88

5.5 Results ...... 90

5.5.1 Movement effects on the epidemic patterns ...... 90

5.5.2 Effects of changing movement patterns ...... 97

5.5.3 Relationship between population density in seasonal areas and epidemic size

...... 103

5.6 Model comparison and validation ...... 104

5.6.1 Comparison of the simulated epidemics with survey data ...... 104

5.6.2 Comparison of the simulated results with previous model ...... 105

5.7 Discussion ...... 107

Chapter 6: Conclusion...... 109

6.1 Summary ...... 109

6.2 Future Research ...... 111

References ...... 113

Appendix A: ODD protocol for the model in Chapter 3 ...... 123

Appendix B: Supplementary figure ...... 130

Appendix C: ODD protocol for the model in Chapter 5 ...... 131

List of Tables

Table 3.1. Parameter values used in the experiments for the model ...... 47

Table 3.2. Percentage of simulations in which each run has more than one peak ...... 49

Table 4.1. Descriptive statistics for orbits ...... 70

Table 4.2. Number of pastoralists who keep or change their orbits ...... 74

Table 5.1. Orbits for mobile agents ...... 84

Table 5.2. Parameter values used in model simulations ...... 88

List of Figures

Figure 2.1. Illustration of a synthetic trail from the origin to the destination and its flights

...... 12

Figure 2.2. Four common abstractions for the spatial transmission of infectious diseases

...... 17

Figure 2.3. Boids simulation ...... 22

Figure 3.1. Annual transhumance movement paths of 67 pastoralists for the 2007-2008 season and the location of campsites...... 32

Figure 3.2. Seasonal zones ...... 34

Figure 3.3. Flow chart for orbit identification ...... 35

Figure 3.4. 8 transhumance orbits ...... 38

Figure 3.5. An example of a simulated trajectory of an agent in orbit 6...... 39

Figure 3.6. Model assumption ...... 42

Figure 3.7. Results for the first scenario where FMD is initiated on day 1...... 51

Figure 3.8. Results for the second scenario where FMD is initiated on day 31 ...... 52

Figure 3.9. Results for the third scenario where FMD is initiated on day 61...... 53

Figure 3.10. The number of infected animals from 2009 to 2013 based on herder reports of clinical signs of disease ...... 55

Figure 3.11. Screen shots of the model at time step 1, 30, 90 and 120...... 56 xii

Figure 3.12. Number of infected animals for each zone at each time step...... 57

Figure 4.1. Key seasonal areas ...... 67

Figure 4.2. 3D plots of transhumance orbits ...... 71

Figure 4.3. Transhumance orbits in 2007-2012 ...... 72

Figure 4.4. Boxplots of orbit-characteristics ...... 73

Figure 4.5. Annual occupancy of grazing zones...... 76

Figure 5.1. The Far North Region of Cameroon ...... 80

Figure 5.2. The landscape of the model ...... 82

Figure 5.3. Maximum number of infected animals and peak time of epidemic curve per scenario ...... 92

Figure 5.4. Results for the first scenario ...... 93

Figure 5.5. Results for the second scenario ...... 94

Figure 5.6. Results for the third scenario ...... 95

Figure 5.7. Results for the fourth scenario ...... 96

Figure 5.8. Results for the fifth scenario...... 99

Figure 5.9. Results for the sixth scenario where the mobile agents starting the orbits in the removed rainy season area do not move...... 100

Figure 5.10. Results for the sixth scenario where the mobile agents starting the orbits in the removed rainy season area change their orbits ...... 101

Figure 5.11. Results for the seventh scenario ...... 102

Figure 5.12. Relationship between population densities in dry season areas and epidemic sizes ...... 103

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Figure 5.13. The percentage of infected animals from 2010 to 2013 based on herder reports of clinical signs of disease ...... 105

Figure 5.14. Comparison of the simulation results ...... 106

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Chapter 1: Introduction

1.1 Problem context

As infectious diseases are transmitted from individual to individual by direct contact, animal and human movements have a fundamental impact on disease transmission over time and across, between, and within regions (Fèvre, Bronsvoort, Hamilton, &

Cleaveland, 2006). Increasing the movements of individuals, goods, or services globally can cause new infectious diseases to be rapidly spread to the world. Such globalization can bring benefits economically and industrially but acts as a major obstacle to preventing the spread of an epidemic. Middle East respiratory syndrome (MERS) was first identified in Saudi Arabia in 2012 and was present all over the world in 2015.

Thanks to air travel, MERS spread to many countries, including Saudi Arabia, the United

Kingdom, China, South Korea, Australia, and the United States, and was attended by considerable loss of life (CNN, 2014; World Health Organization, 2015).

In the transition between various locations, an individual can get in touch over time with other individuals, which enables the infectious disease to spread. This implies a need to integrate space and time to fully understand the transmission of infectious diseases. Analyzing and predicting individuals’ movements allow us to predict likelihood of future outbreak patterns and to minimize the risk caused by the outbreak.

Epidemiological models of fully mixing populations, however, consider only one dimension of the disease transmission - the time dimension. Specifically, the models only analyze the temporal progress of an epidemic and assume populations where all individuals have an equal chance to contact each other. Researchers have recently developed a variety of methods to address these issues by incorporating space-time heterogeneity into their models (Dion, VanSchalkwyk, & Lambin, 2011; Doran &

Laffan, 2005; Ferguson, Donnelly, & Anderson, 2001; Kao, 2003; Keeling et al., 2001;

LeMenach et al., 2005; Tildesley et al., 2008; Ward, Laffan, & Highfield, 2009).

Because individuals have different contacts at any given time and the contacts change consecutively depending on movements, disease models to incorporate dynamic individual movements need to take into account the level of individual heterogeneity in contacts over time that prior population-based models do not consider. To implement this, agent-based modeling (ABM) provides the role of a suitable tool for implementing individual heterogeneity. Advances in the ABM literature have also shown much promise in representing heterogeneous populations (Eubank et al., 2004; Mao & Bian, 2011;

Torrens & Benenson, 2005).

Thus, this dissertation investigates spatial and temporal dynamics of disease transmission by exploring the impact of human and animal movements on disease transmission. In particular, I analyze pastoralist mobility patterns and propose movement rules for mobile pastoralists. I also develop an agent-based movement model coupled with a disease transmission model to simulate the spatiotemporal dynamics of foot-and-

2 mouth disease (FMD) and examine how pastoralist mobility affects disease transmission in the study area.

1.2 Research Objectives

The overall objective of this dissertation is to understand the movement of pastoralists and its impact on disease transmission in the Far North Region of Cameroon. More specifically, the specific objectives of this dissertation are the following:

1) Develop an ABM to examine the impact of seasonal movements and daily grazing

activities of mobile pastoralists on the transmission of FMD in the Far North

Region of Cameroon.

2) Empirically examine pastoralists’ mobility patterns using transhumance surveys

and categorize the patterns to derive the mobility rules for agents.

3) Extend the first ABM by including sedentary pastoralists and diverse mobility

patterns of mobile pastoralists to investigate dynamic epidemic patterns

depending on the variation of the pastoralists’ mobility patterns.

1.3 Dissertation Overview

This dissertation consists mainly of three independent papers. The remainder of this dissertation is organized as follows.

Chapter 2 reviews extensive current research related to the topic of this dissertation including human and animal mobility pattern analysis, modeling human behavior, modeling epidemic process, agent-based modeling, and FMD. Chapter 3

3 develops an ABM coupled with an epidemic model to examine the impact of the movements of mobile pastoralists on FMD transmission in a transhumance system in the

Far North Region of Cameroon. This chapter corresponds to the first objective above.

This chapter has been published as Kim et al. (2016). Chapter 4 examines pastoralists’ mobility patterns using data collected over a five-year period and proposes behavioral parameters for animal/herd movement rules that are used for the mobility rules for agents.

This chapter corresponds to the second objective above. Chapter 5 develops a follow-up model of the first ABM by including various scenarios with different herd population composition (i.e. mobile herds only, mobile and sedentary herds), different pastoralist movement patterns, and different disease transmission related factors (i.e. secondary infection, carriers, infant immunity, and new births). This chapter corresponds to the third objective above. Chapter 6 is the conclusion of the dissertation. This chapter summarizes the dissertation, highlights its contributions, and discusses future work.

Chapter 2: Literature Review

This chapter reviews existing studies related to the topic of this dissertation including human and animal mobility pattern analysis, modeling human behavior, modeling epidemic process, agent-based modeling, and FMD.

2.1 Human/Animal Mobility Pattern Analysis

The description of animal/human mobility differs from field to field. Disciplines such as Anthropology, summarize the animal/human behavior data through several descriptive statistics and tries to provide some basic intuition or conceptual framework for reasons why animals/humans move the way they do. One of the frameworks includes the explanation that pastoralists move with their livestock to take advantage of the seasonal appearance of vegetation and to minimize the risk of losing their livestock because of drought, diseases, and other disasters (Barﬁeld, 1993; Behnke, Fernandez-

Giminez, Turner, & Stammler, 2011; Butt, 2010; Dwyer & Istomin, 2008; Moritz et al.,

2010; D. Stenning, 1957; Turner, McPeak, & Ayantunde, 2014). These disciplines study pastoralist mobility at different spatial and temporal scales. Moritz et al. (2010) examine spatiotemporal variation in daily herd movements and grazing pressure at a micro scale.

By utilizing GPS technology and GIS analytical tools, they collect daily herd movement data of mobile pastoralists during dry season in the Logone floodplain of Cameroon. 5

Similarly, Butt (2010) explores how cattle’s daily movement and grazing behavior vary in different seasons by conducting a case study of Maasai pastoralists. He also collects cattle tracking data using GPS. Both studies conduct descriptive analysis and provide robust geographical and behavioral interpretation of pastoral livestock mobility at a micro scale. These disciplines also include macro studies. Pastoralist mobility analysis at a coarse spatial and temporal scale, such as annual scale, mainly depends on pastoralists’ survey or ethnographic material (Dwyer & Istomin, 2008; Moritz, Scholte, Hamilton, &

Kari, 2013).

Unlike the micro-scale studies mentioned above, macro-scale studies focus on describing and explaining the factors that affect pastoralist mobility (Barﬁeld, 1993;

Behnke et al., 2011; Dwyer & Istomin, 2008; Galvin, 2009; Moritz et al., 2013; D.

Stenning, 1957). Pastoralists have adapted and are adapting to social, political and environmental changes. Galvin (2009) describes one of the main causes of changes in the pastoral systems, which is the dissection of a natural system by socioeconomic factors such as land tenure change, livelihood changes, sedentarization, and social capital/institutions. Behnke at al. (2011) identifies the ecological, socio-economic and cultural factors that affect the movement of pastoral systems through the three case studies in the semi-arid tropics of sub-Saharan Africa, in temperate Asia, and in the

Arctic.

Fields such as Ecology, Physics or Computer Science take a different approach.

To explain human/animal mobility, they use a more rigorous statistical analysis and try to find a statistical distribution that fits the data. Once they know the distribution which the

6 data follows, then they can predict the future human/animal behavior based on the statistical properties of the specific distribution. Recent studies claim that animal movements are described by the statistics of Lévy flights, in which the distribution of step lengths is heavy tailed, rather than by Gaussian statistics, which have traditionally been used in modeling of animal movements because they are mathematically tractable.

Bartumeus et al. (2005) analyze the statistical differences between two random- walk models commonly used to fit animal movement data: correlated random-walk

(CRW) and Lévy walk (LW). CRW model is constructed by an exponentially decaying distribution of step lengths (i.e. displacement events) with a non-uniform angular distribution of turning angles (i.e. deviations from the previous direction). The step lengths (l) of the CRW model are randomly drawn from a Gaussian distribution centered at the minimum step length l0 = 1 and with fixed standard deviation σ = 1. The turning angle is drawn from the wrapped Cauchy distribution (WCD), which is typically used as a probability distribution of turning angles, by inserting a uniform random variable, 0 ≤ u

≤ 1. Finally, the angle deviation θ is obtained from the following formula:

1 − 휌 1 휃 = 2arctan [( ) tan [휋 (푢 − )]], 1 + 휌 2 where ρ is the shape parameter of the WCD which controls sinuosity. Thus, the relative straightness of the CRW changes by varying the shape parameter ρ. When ρ = 0, a uniform distribution with no correlation between successive steps is obtained, and

Brownian motion results.

Lévy-walk (LW) model is based on a uniform distribution of the turning angles with a power-law distribution of step lengths, which are called flights. The step length l follows a power law distribution P(l) = l-μ with 1< μ ≤ 3 (Viswanathan et al. 1999). In this study, the step lengths are generated by sampling from a power-law distribution in the following way:

(1−휇)−1 푙 = 푙0푢 , where l0 is the minimum step length (i.e. flight) and μ denotes the power-law exponent.

Since μ reduces the probability of long travels, the directional persistence in the movement increases with μ. Thus, when μ ≥ 3, Brownian motion is obtained.

Through a set of simulations for the behavior of a relevant macroscopic property of random walks, Bartumeus et al. (2005) show that the macroscopic statistical properties of CRW do not fit the best optimal random searches at a large enough spatiotemporal scale. When ρ < 1, even ρ is very close to 1, the macroscopic behavior of movement converges to the Brownian motion. On the other hand, LW shows a whole variety of super-diffusive behaviors and a gradual transition from normal diffusion (i.e. μ ≥ 3) to ballistic motion (i.e. μ → 1). Therefore, LW is a proper model to depict scale-free animal movements.

However, the use of LW to describe animal movement is still subject to some controversy, and recent studies suggest that the Lévy model is less applicable to model animal movement (Benhamou, 2007; Pyke, 2015). Benhamou (2007) argues that the observed patterns that are attributed to Lévy processes can be generated by a simpler composite random walk process where the turning behavior is spatially dependent. He

8 also points out unreality of the assumptions in LW modeling. First, the assumption that resources are uniformly distributed in the natural environment is not empirically valid.

The assumption of infinite variance (i.e. the distribution of step lengths is infinite) is also unrealistic because LW searches are truncated whenever a target is located. Pyke (2015) also argues the controversy regarding statistical methods of Lévy walk model and criticizes its biologically unrealistic.

Human movements can be described by various stochastic processes based on the movement purpose. Random human behaviors can be approximated by a Poisson process

(Barabasi, 2005). On the other hand, according to many recent studies, human mobility, especially in the case of travel for work or leisure, can be better explained by a heavy tail distribution such as Lévy flight, Pareto, log-normal, and Weibull (Brown, Liebovitch, &

Glendon, 2007; Gonzalez, Hidalgo, & Barabasi, 2008; Rhee et al., 2011). The easy accessibility of various human mobility datasets makes the analysis of human behavior broader and more accurate.

Brown et al. (2007) provide evidence that human movements can be described by the statistics of Lévy flights. They use hunter-gatherer foraging data which are from a book on hunters’ settlement patterns and camp structure, and analyze the geographic distances between camps (i.e. step lengths). By fitting different probability distributions to the data and examining the fit using One-sample Kolmogorov–Smirnov tests, they conclude that the power law distribution of the step lengths is the best fit with an exponent of −1.9675 (r2=0.965). Although this study constructs and uses its own dataset, the reliability of their data is questionable. The reason is that the step lengths, i.e. the

9 geographic distances between camps where the distance unit is kilometer, are converted from the measured distance on the printed maps where the distance unit is millimeter. So, the data are subject to a large measurement error.

Gonzalez et al. (2008) use tracking information of 100,000 mobile phone users to analyze human mobility. They show that the distribution of step lengths over all users is well approximated by a truncated power-law distribution:

1−휇 푃(푙) = (푙 + 푙0) exp (−푙/훫), where K denotes a cutoff value. K truncates human mobility to limited space and makes the model more realistic. Even though this study uses a large amount of mobility data, the problem of data accuracy still remains, because the location of a user is approximated by the user’s location from the nearest cell phone tower. Also, the location can be tracked only when a call is made. Thus, tracking information by using mobile phone users cannot fully capture human mobility.

Rhee at al. (2011) analyze the mobility patterns of humans using mobility track logs obtained from GPS receivers which take a reading of their current positions every

10s with a three-meter position accuracy. To take account of various situations (i.e. randomness), they collect the data from five different regions: two university campuses,

New Your City, Disney World, and one state fair. They first fit various distributions to the GPS traces by maximum likelihood estimation and quantify them using Akaike’s information criterion (AIC). All traces except Disney World have the best fit with truncated power-law, whereas Disney World has the best fit with the lognormal

10 distribution. These results show that human walk patterns contain statistically similar features observed in Levy walks, even though human walks are not random walks.

Xiao et al. (2015) analyze the spatial and temporal characteristics of pastoral mobility in the Far North Region of Cameroon and categorize the transhumance movement trajectories into three groups based on the shape of the trajectories. Finally, they develop a spatial-temporal mobility model to estimate the probability of a mobile pastoralist being at a location at any time.

A substantial body of the literature on human mobility assumes that mobility occurs in nature, i.e. a continuous Euclidean space. A considerable amount of human mobility, however, occurs in a constrained discrete space. Some papers have attempted to analyze human mobility within specific environments. For example, Jiang et al. (2009) investigate human mobility in a large street network from the perspectives of trails and flights using a GPS dataset collected from 50 taxicabs for six months. The distribution of

−2.5 trail lengths follows a power-law distribution, i.e., 푃(푙푇) ∝ 푙푇 , with a cutoff value 3 km. A flight represents part of a trail, which can be linear or curved (see Figure 2.1). The flights are extracted from the trails, and the distribution of flight lengths fits a power-law

−2.3 −휆푙퐹 distribution with an exponential cutoff λ, i.e., 푃(푙퐹) ∝ 푙퐹 푒 . For both cases, the power-law exponent μ is between 1 and 3. This indicates that human mobility in a street network exhibits a Lévy flight behavior.

Figure 2.1. Illustration of a synthetic trail from the origin to the destination and its flights (Jiang, Yin, & Zhao, 2009)

2.2 Modeling Human Behavior

Modeling human behavior have been studied in various fields such as network flow problems, traffic assignment problems, and are generally categorized into two; macroscopic and microscopic models (Hamacher, 2001).

Macroscopic models appear in network flow or traffic assignment problems and take optimization approach using node-link-based graphs as the data format. They consider pedestrians as a homogeneous group to be assigned to nodes or links for movements and do not take into account the individual interactions during the movement.

On the other hand, microscopic models emphasize individuals’ behavior and their interaction and physical environments such as walls and obstacles. Microscopic models are mainly based on simulation and use fine-grained grid cells as the base format for simulation. Different micro-simulation models have been proposed over the last decades 12

(Schadschneider, 2001), but two approaches are getting attention; social force model and floor field model.

A frequently cited model of the former type is advanced by Helbing and colleagues (1995) and is based on strong mathematical calculation acted on agents to determine its movement to the destination. The social force model considers the effects of each pedestrian upon all other pedestrians and physical environment. Pedestrians have a particular destination and a preferred walking speed. The motion of a pedestrian is determined by its tendency to maintain its speed and direction and interaction with other pedestrians and physical barrier. The general equation of motion of a pedestrian i is

⃗⃗ ⃗⃗ (푎푐푐) ⃗⃗ (푠표푐) 푭푖(푡) = 푭푖 + 푭푖 (푡) + 휉푖(푡).

0 The tendency to maintain the desired walking speed vi and desired direction ei is

(acc) expressed by the first force term Fi , which reads

⃗⃗ (푎푐푐) 0 푭푖 = (푣푖 푒 푖 − 푣 푖)/휏푖,

(soc) where vi is actual velocity and τi is the reaction time of i. The social force Fi which describes the influence of the environment, is composed of terms, expressing the interaction with other pedestrians and barriers, respectively. The interaction with other pedestrians is described by a repulsive potential and by an attractive potential. The

(rep) repulsive force Fij to avoid collisions between pedestrian i and pedestrian or border j is

⃗⃗ (푟푒푝) 푭푖푗 = −∇푟 푖푗푉푖푗(‖푟 푖푗‖). with a repulsive and monotonic decreasing potential 푉푖푗(‖푟 푖푗‖). The vector 푟 푖푗 = 푟 푖 −

푖 푖 푟 푗 has been introduced, where 푟 푖 denotes the actual position of pedestrian i and 푟 푗

13 denotes the location of individual or border j that is nearest to pedestrian i. The attractive

(acc) force Fik at place 푟 푘 can be described in a similar way to the repulsive force as follows:

⃗⃗ (푎푡푡) ‖ ‖ 푭푖푘 (푡) = −∇푟 푖푘푊푖푘( 푟 푖푘 , 푡), with attractive and monotonic increasing potential 푊푖푘(‖푟 푖푘‖). The noise ξi(t) is added to account for random variations of the behavior. With this simple framework it is possible to predict realistic scenarios such as pedestrian crowds in normal and evacuation situations. However, this model leads to the computation of O(n2) complexity, which is unfavorable for computer-based simulation with many agents (Henein & White, 2004).

This model has been extended to an active walker model for self-organizing pedestrian movement (Helbing, Molnár, Farkas, & Bolay, 2001; Helbing, Schweitzer,

Keltsch, & Molnár, 1997). Here a walker leaves a trace by modifying the underground on his path. The spatiotemporal distribution of the existing traces is described by a ground potential as follows:

푑퐺(퐫, 푡) 1 = [퐺 (퐫) − 퐺(퐫, 푡)] + ∑ 푄 (퐫 , 푡) × 훿(퐫 − 퐫 (푡)). d푡 푇(퐫) 0 푖 푖 푖 i

Due to chemical decay, the ground potential has a certain lifetime T(r). Therefore, the existing trails tend to return to its natural ground conditions G0(r) by fading gradually.

New traces created by another walker i is described by the term Qi (ri, t) δ(r – ri) where

Dirac’s delta function δ(r – ri) makes a contribution only at the actual position ri(t) of the walker. The trail potential Vtr for a walker, which reflects the attractiveness of a trail from the actual position ri(t) of the walker, is specified as follows:

‖푟−푟 ‖ − 푖 2 휎(푟 ) 푉tr(푟푖, t) = ∫ 푑 푟 푒 푖 퐺(푟, 푡), where σ(ri) denotes the range of visibility.

Burstedde et al. (2001) have proposed floor field model using a two-dimensional cellular automaton, where two kinds of fields - static and dynamic - are introduced to translate social force model’s long-ranged interaction of pedestrians into a local interaction. Although this model considers only local interactions, they showed that the resulting global phenomena share properties from the social force model such as lane formation, oscillations at bottlenecks, and fast-is-slower effects.

The basic data structure of floor field model is grid cells and each cell represents the position of an individual and contains two types of numeric values which the individual consults to move. These values are stored in two layers; static field and dynamic field. A cell in the static field indicates the shortest distance to an exit. An individual is in a position to know the direction to the nearest exit by these values of its nearby cells. While the static field has fixed values computed by the physical distance, the dynamic field stores dynamically changing values indicating individuals’ virtual traces left as they move along their paths and its equation is as follows:

훿퐹 = 퐷Δ퐹 − 훿퐹, 훿푡 where D is the diffusion constant and δ is the decay constant. It is similar to the ground potential in active walker model in terms a pedestrian leaves a trace by modifying the underground on his path. The trace in the floor field model, however, differs in the fact that it depends on chemotaxis while it depends on only visibility in the active walker

15 model. The floor field model uses grid cells as the data structure and computes movement of an individual at each time step choosing the next destination among adjacent cells, and it makes computer simulation more effective.

2.3 Modeling Epidemic Process

Movement patterns of hosts during outbreaks of directly transmitted infectious diseases such as FMD are very important. The reason is that the probability of disease transmission is largely influenced by hosts’ movements. The traditional epidemic models

(i.e. population-based models), however, have difficulty in explaining heterogeneities in the location and movement of hosts. Researchers have recently extended the classical population-based model in various ways to incorporate spatial heterogeneities. Riley

(Riley, 2007) identifies four approaches that are used in spatially explicit models of infectious disease transmission (Figure 2.2). For patch transmission (Figure 2.2A), the population is assumed to be fully-mixing and each individual receives the same force of infection. Durand and Mahul (2000) simulate epidemic dynamics with two distinct

French regions: high-density area and low-density area. The simulation shows that higher density patch is greatly affected by disease transmission than lower density patch. This implies that spatial heterogeneity in host density plays an important role in disease transmission. Patch models, however, do not take into account host movement across patches. Moreover, spatial homogeneity issue within a patch still remains.

Figure 2.2. Four common abstractions for the spatial transmission of infectious diseases (Riley, 2007)

To incorporate spatial heterogeneity at a smaller spatial scale and represent discrete individual transmission, individual-based models are introduced and are extended in various forms. First, spatially explicit distance-transmission models (Figure

2.2B) assign each farm to an individual and assume that infectious individual can infect all susceptible individuals within a certain time period (Keeling et al., 2001; Riley, 2007;

Tildesley et al., 2008). In these models, the probability of infection depends on a monotonically decreasing function of distance between individuals. In the model proposed by Keeling et al. (2001), transmission between individuals is determined not only by the number and type of animals, but also by the distance between the susceptible and infected farms. The rate at which an infectious farm j infects a susceptible farm i is as follows:

푟푎푡푒푖푗 = 푆푖 ∑ 푇푗 × 퐾(푑푖푗) 푗∈푖푛푓푒푐푡푖표푢푠

푆푖 = ∑ 푠푠푛푠,푖 푠ϵ푠푝푒푐푖푒푠

푇푗 = ∑ 푡푠푛푠,푗, 푠ϵ푠푝푒푐푖푒푠 where ns,i is the number of livestock species s on farm i, ns,j is the number of livestock species s on farm j, Si and Tj refer to the species-specific susceptibility and transmissibility, respectively, dij is the distance between farms i and j, and K is the transmission kernel. Using this model, Keeling et al. (2001) assess disease control strategies such as contiguous farm culling. This model is also used to assess another disease control strategies by Tildesley et al. (2006) by assuming that vaccination takes place within an annulus (defined by an inner and outer radius) around each index premises. Tildesley et al. (2008) utilize Keeling et al.’s model to examine the model accuracy by comparing it with the 2001 FMD epidemic data in the UK. Although their model slightly overestimates the number of infected animals, it is relatively in line with the 2001 epidemic data at the individual farm level.

Another type of individual-based models is network transmission model (Figure

2.2C, D) where a network structure is used to describe individuals and their interaction by assigning each individual a node and connecting nodes by links (i.e. an individual becomes the modeling unit) (Bian & Liebner, 2007; Bian, 2004; Christley et al., 2005;

Keeling, Danon, Vernon, & House, 2010; Kiss, Green, & Kao, 2006a; Xu & Sui, 2009).

The nodes and links form the social network of the host population, which directly affects disease dynamics. Consequently, the structure of social network determines how disease spreads. Xu and Sui (2009) investigate the relation between the structure of social network and disease transmission. By introducing randomness (ϕ) into an otherwise

18 regular network, they construct three different structures of networks: a completely regular network (ϕ = 0), a completely random network (ϕ = 0), and a small world network (0< ϕ <1). The small world model, initially proposed by Watts and Strogatz

(1998), is used to investigate the spread of an infectious disease and the functional significance of small world connectivity (Christley et al., 2005; Kiss, Green, & Kao,

2006b). Through simulating disease transmission on three networks using agent-based approach, Xu and Sui (2009) find that epidemic on the small-world network produces biggest epidemic size in a short time period. This implies that infectious diseases spread much more easily and quickly in a small world than in a completely regular or completely random network.

To explore the impact of movement patterns on FMD epidemic dynamics,

Keeling et al. (2010) apply commuting behaviors through network, which are characterized by individual recurrent movements between connected locations. They compare two different movements: commuter movements to represent regular patterns, and random movements to represent irregular patterns or to include potential biases.

However, they cannot capture noticeable changes from the predicted epidemic dynamics for the two movements.

Cellular automata (CA) model is also one type of individual-based models. This model divides space into cells and each cell represents a discrete individual (Bian, 2013).

It also takes into account local interactions of individuals by allowing them only to interact with neighboring individuals. The interactions are based on a set of rules, which makes modeling relatively simple. Building on the CA model, Doran and Laffan (2005)

19 examine the spatial dynamics of FMD outbreak in feral pigs and neighboring livestock species in Queensland, Australia. To represent feral pig home range, a cell size of 29 km is chosen. They assume that herds within cells are homogeneous but they differ between the cells. The model is implemented to two regions where population density is different.

The model results produce the spatial pattern of FMD spread and describe the effects of population density on disease outbreak.

The last type of individual models is an individual-based mobile model, which is typically realized using agent-based approach. This model is basically similar to the network model regarding individuals being the modeling unit and individuals interacting with each other. The only novel feature is that this model can take into account individual’s mobility. Mao and Bian (2011) propose a simulation model to explore the diffusion process of influenza. A contact network is modeled to represent the diffusion.

By integrating the network model into an agent-based approach, they implement the mobility of individuals.

The cases that have been applied agent-based approach on FMD transmission is rare. Dion et al. (2011) develop an object-based model, named EPIFMD (EPIdemiology of FMD) to explore how landscape heterogeneities (i.e. wildlife and livestock) influence the epidemiology of FMD in southern Africa. The model is simulated direct contacts between agents assigned as wildlife and livestock. However, limitation remains that the model has not been validated due to a lack of calibration data.

FMD transmission has been modeled in various approaches as well as the individual models. A recent review article classifies the FMD models in terms of control

20 strategy, resolution of models and data, and study area through systematic literature review (L. W. Pomeroy et al., 2015). This study reveals that modeling methodologies have been well developed to describe transmission and control of the virus, while host and disease data are not sufficient to quantify parameter values. For better understanding

FMD transmission, novel data sources need to be incorporated into the models and multiple endemic areas should be modeled.

2.4 Agent-based Modeling

Agent-based modeling (ABM) is a computational model for simulating interactions of autonomous agents in a given environment. Since the 1990s it has become increasingly popular and has been widely used in social sciences to study a wide range of phenomena

(Epstein, 1999; Gilbert, 2008; Macal & North, 2005; Railsback & Grimm, 2010).

Phenomena that we need to analyze and model are complex. They are represented by cumulative patterns or behaviors at the macro-level that define characteristics of real systems and therefore they indicate essential underlying processes and structures (Volker

Grimm et al., 2005). For this reason, it is inherently difficult to explain complex phenomena directly from the micro elements.

ABM represents a bottom-up approach to understand and predict the dynamics of a system by incorporating multiple patterns (Epstein, 2006; Russell, Norvig, Canny,

Malik, & Edwards, 2003). Collecting and accumulating information about individual agents at the micro level of the system, ABM formulates agents’ behavior. Here, an agent is defined as an identifiable and discrete individual that interacts with other agents in its

21 environment, which is represented by a physical or artificial space (Epstein, 2006;

Gilbert, 2008; Macal & North, 2005). Each agent can move or act based upon its own preferences or own rules of action to achieve its goal. Agent learns based on its own experiences and adapts its behaviors to the environment. Multiple local behaviors that agents form at the micro scale give rise to the overall pattern of the system at the macro scale (Epstein, 2006; Gilbert, 2008; Railsback & Grimm, 2011).

Reynolds (1987) explores agents’ interaction characterized by simple behavioral rules. Author obtains emergence by simulating paths of each bird individually. In his model, each agent, which represents a bird, has three movement rules to avoid collisions with nearby flockmates, to match velocity with nearby flockmates, and to stay close to nearby flockmates. With these simple rules applied at the individual level, flock pattern can be described (Figure 2.3).

Figure 2.3. Boids simulation (Macal and North 2005)

ABM is often compared with a mathematical or an equation-based model (EBM) in many fields (Parunak, Savit, & Riolo, 1998). EBM identifies system variables and evaluates them using a set of equations. However, it typically lacks consideration of individual heterogeneity because EBM employs aggregate agent equations. This makes it hard to understand the relationships between variables and how they affect phenomena individually. On the other hand, ABM consists of a set of agents that allow modeling individual heterogeneity. It enables researchers to analyze complex phenomena at multiple scales, to obtain the emergences of a structure at the macro-scale from an individual level, and to simulate adaptation and learning of agents. (Epstein, 2006;

Parunak et al., 1998).

2.5 Foot-and-Mouth Disease

Foot-and-mouth disease (FMD) is a highly contagious viral disease that affects cloven- hoofed animals such as cattle, pigs, sheep and goats (Soren Alexandersen & Mowat,

2005; Grubman & Baxt, 2004). The virus was first recognized and described as a viral pathogen of animals by Loeffler and Frosch (1898). FMD virus has been distinguished in seven serotypes (A, O, C, Asia 1, and South African Territories 1, 2, and 3) (Grubman &

Baxt, 2004; Kitching, 2005).

FMD virus is spread through various routes. One of the most common ways is the movement of infected animals and their direct contact with susceptible animals. Through abrasion on the skin or mucous membranes, susceptible animals may be infected. Since

23 many routes of viral entry may be involved at the same time, transmission by direct contact can be very rapid (Kitching & Alexandersen, 2002; Kitching, 2002).

The virus can also be transmitted by aerosol depending on temperature and humidity that usually occurs during a close contact between susceptible and infected animals. Cattle is most likely to be infected by an aerosol virus because of relatively large respiratory volume and high susceptibility compared to other species (Kitching, 2002).

Sheep and goats are highly susceptible to infection with FMD virus by the aerosol. Their lower respiratory volume, however, produces considerably less aerosol and makes them less likely to become infected by airborne virus (Kitching & Hughes, 2002). Pigs are considerably less susceptible to aerosol infection than ruminants, but they produce more aerosol virus than ruminants (Kitching & Alexandersen, 2002).

Animals can be infected though indirect contact such as by eating virus contaminated products or by being placed in a heavily contaminated environment. FMD virus attached to a Wellington boot in soil has been reported to survive up to 12 years. It can also survive for at least a year at the temperature of 4°C (Mahy, 2005).

Lastly, FMD virus can be spread by carrying on clothes or shoes of people that have had contact with infected animals and vehicles that have visited infected farms.

Milk or animal products such as frozen bone marrow and lymph nodes may be the means of spread of the virus, as well (Mahy, 2005).

The incubation period for FMD depends on the animal species, infecting dose, strain of virus, route of infection, individual susceptibility and husbandry conditions.

After certain period of incubation, animals show clinical signs. Infected animals are lame,

24 develop fever, and prefer to lie down. Lesions and vesicles on tongue and feet are the most frequent signs in infected animals (Soren Alexandersen & Mowat, 2005; Kitching

& Alexandersen, 2002; Kitching, 2002).

The initial diagnosis for cattle and pigs is based on clinical signs, with or without a history of contact with infected animals (Kitching & Alexandersen, 2002; Kitching,

2002). Clinical diagnosis for sheep and goats, however, is difficult because the appearance of a lesion is transient and the symptoms are similar to other diseases. Thus, laboratory confirmation of diagnosis of FMD is essential. If a vaccine has been used on the animals, then it is hard to distinguish between an antibody resulting from infection or vaccination. In endemic regions in cattle that have partial natural or vaccinal immunity, clinical signs may be mild and may be missed (Kitching & Hughes, 2002).

FMD outbreak causes significant economic damage in terms of losses of livestock products and costs of disease control. Moreover, FMD-infected countries are restricted to trade livestock products to FMD-free countries (James & Rushton, 2002). Estimated economic costs to agriculture and industries of FMD outbreak in the United Kingdom

(UK) in 2001 was about ₤6 billion. This outbreak not only resulted in major economic losses but also left a negative impact on public opinion in the UK and in Europe

(Thompson et al., 2002).

FMD is endemic to almost all countries of sub-Saharan Africa, where pastoral systems predominate (Vosloo, Bastos, Sangare, Hargreaves, & Thomson, 2002). Due to inadequacy or lack of disease surveillance systems, outbreaks are not properly reported and/or documented in these regions. Moreover, livestock owners and animal health

25 authorities in most of the African countries do not regard FMD as a serious disease because of its less severe direct economic impact compared to other animal diseases. For these reasons, FMD is endemic to many African countries. The Far North Region of

Cameroon is also in an endemic situation of FMD with most outbreaks caused by serotypes A and O in cattle (Ekue, Tanya, & Ndi, 1990; Vosloo et al., 2002).

Chapter 3: Simulating the Transmission of Foot-and-mouth Disease among Mobile Herds in the Far North Region, Cameroon

3.1 Introduction

Food-and-mouth disease (FMD) is a highly contagious viral disease in cattle and is known to cause problems such as decreased livestock productivity and decreased access to lucrative international markets for animals and animal products (Knight-Jones &

Rushton, 2013). The FMD virus is transmitted by close contact with infected animals, as well as through contaminated environments and people, and possibly through air over long distances (S. Alexandersen, Zhang, Donaldson, & Garland, 2003). Recent studies have found an endemic environment of FMD in Cameroon where pastoralists make seasonal transhumance movements with herds of cattle (Bronsvoort et al., 2003; Ludi et al., 2014; Laura W Pomeroy et al., 2015; Wint & Robinson, 2007). Researchers have pointed out that the movement of infected animals in non-endemic settings of Europe has played a significant role in the dynamics of FMD transmission in general (Fèvre et al.,

2006) and in endemic settings in sub-Saharan Africa in particular (Bronsvoort, Tanya,

Kitching, Nfon, & Hamman, 1990; Rweyemamu et al., 2008; Vosloo et al., 2002) The movements of transhumant pastoralists create a highly heterogeneous contact network in space and time between FMD hosts. While population-based evidence suggests that

27 transhumance increases FMD risk (Bronsvoort et al., 2004), the hypothesis that mobile herds maintain endemic diseases such as FMD has not been evaluated directly for the individual case.

In this paper, we investigate the dynamics of FMD transmission between mobile herds in the Far North Region of Cameroon using a combination of field data and an agent-based model. We hypothesize that diseases without significant environmental persistence or long-term asymptomatic carriers cannot be maintained in mobile herds alone without the possibility of re-infection from other sources such as sedentary herds.

With an ultimate goal of modeling FMD dynamics for the entire region, we start by focusing on mobile herds in isolation to determine whether mobile herds can sustain

FMD transmission. Answers to this question will advance our understanding of disease dynamics in mobile pastoral systems.

Spatial and temporal heterogeneity in host density plays an important role in disease transmission and it is therefore critical to capture the dynamics of contact patterns in the region before we can effectively model the transmission of the disease. While different approaches have been developed in the literature to incorporate heterogeneity into epidemiological models for infectious diseases (Doran & Laffan, 2005; Kao, 2003;

LeMenach et al., 2005; Riley, 2007; Tildesley et al., 2008), few have incorporated dynamic contact networks such as transhumance of mobile pastoralists. Because individuals have different contacts at any given time and the contacts change consecutively for the entire network depending on the individuals’ movements, prior

28 population-based models do not take into account this level of individual heterogeneity in contacts over time.

The network-based methods, address the heterogeneity of contacts among individuals by describing the contact structure as a network formed by nodes, representing hosts, and edges representing the contacts, or better, the distance between hosts (see also Bian & Liebner, 2007; Bian, 2004; Keeling et al., 2010; Kiss et al.,

2006b). In our case, the contact network constantly changes because the herds continuously move. For this reason, we develop an agent-based model to help capture the dynamic contacts between individual mobile herds over time. Agent-based models

(ABMs) have been used in many epidemiological studies (Barrett C, Bisset K, Eubank

SG, Feng X, & Marathe, 2008; Eubank et al., 2004).

Previous published models have incorporated heterogeneity in a variety of ways to examine spatiotemporal dimensions of FMD transmission. Dion et al. (2011) developed an object-based model, named EPIFMD (EPIdemiology of FMD) to explore how landscape heterogeneities (i.e., wildlife and livestock) influence the epidemiology of

FMD in southern Africa. Bates et al. (Bates, Thurmond, & Carpenter, 2003) introduced a spatial stochastic epidemic simulation model using Monte-Carlo simulation to evaluate eradication strategies of FMD in California. Using UK 2001 FMD epidemic data,

Ferguson et al. (2001) demonstrated movement restrictions would be effective to control the outbreak. Keeling et al. (2001) introduced an individual farm-based stochastic model and showed that the spatial distribution of farms as well as size and species compositions of farms have an effect on outbreak patterns in space and time when the farms remain in

29 constant locations. While Ferguson et al. (2001) looked generally at changes to contact structure or transmissibility of FMD over time and the others added aspects of random stochasticity to contacts, but none treated the contact network as fully dynamic based on known patterns.

In our model, a camp with multiple pastoral households and herds is represented as one agent that has its own movement rules and we derive these rules from our transhumance survey data (Moritz et al., 2010, 2013; Xiao, Cai, Moritz, Garabed, &

Pomeroy, 2015). In the model, we identify the mobile pastoralists that have contact with each other during transhumance and use an epidemiological model to simulate disease transmission within and between herds. The model allows us to answer the question whether an FMD endemic can be sustained in mobile pastoralists’ herds in the region without having interaction with other infection sources.

In the remainder of this paper, we discuss the study area and the collection of movement data from the pastoralist population in Section 3.2.1. The details of the agent- based model and the epidemiological model are discussed in Section 3.2.2 and in the appendix A. Computational experiments and comparison of the model to data are presented in Section 3.3. We conclude the paper with a discussion of our finding that mobility plays a critical role in disease transmission and an evaluation of our modeling approach.

3.2 Data and Methods

A critical step in developing the agent-based model (ABM) is the understanding of how the agents move in our study area. In this section, we first describe the data and analysis and then we discuss the ABM for FMD transmission in the herds using a susceptible- infected-recovered (SIR) model where the contacts between individual herds are dynamically computed through the simulation.

3.2.1 Spatial and Temporal Movements of Pastoralists

The Far North Region of Cameroon has a semi-arid climate which has four seasons: rainy, cold dry, hot dry and transition season (Moritz et al., 2013). Seasonal changes allow long-range movements of pastoralists between ecological zones where pastoralists move about 100-250 km. Transhumance allows pastoralists to take advantage of the changes in the spatiotemporal distributions of forage and water and maximize grazing for their livestock during the dry season. This is usually referred to as transhumance (D.

Stenning, 1957). Mobile pastoralists in the Far North Region move with their livestock between rainy season and dry season pastures. During the rainy season (June to

September), pastoralists are in the south of the region. At the end of the rainy season, they move along transhumance routes to the Logone floodplain which has abundant grass during the cold dry (October to January) and hot dry seasons (February through May)

(Moritz et al., 2010).

Figure 3.1. Annual transhumance movement paths of 67 pastoralists for the 2007-2008 season and the location of campsites that they stay during each season (sojourn sites) and between seasons (transit sites).

We have conducted transhumance surveys to document how pastoralists move in the region. In this survey, pastoralists were asked to recall their daily locations of the previous year and how long they stayed in each location (Moritz et al., 2013; Xiao et al.,

2015). The data set allows us to reconstruct the spatial and temporal trajectories of the pastoralists. In general, there are several groups of pastoralists who follow similar transhumance routes according to the location of their campsites and timing (i.e., where the groups are at a point of time and how long they stay at the point). Each of these groups is called a camp and 67 camps were surveyed in the data in the year 2007-2008

(Figure 3.1). Based on the survey data we identified whether pastoralists’ movements occur during a particular season or whether pastoralists are in transit between seasonal grazing areas. The pastoralists have their seasonal grazing areas where they tend to stay at sojourn campsites for longer periods (typically >20 days) before they move to another location. When pastoralists move between these zones, they typically stay only for a few days in transit campsites along the transhumance corridors.

In order to understand the movement patterns of the pastoralists, we first identified the grazing zones and then detected the sequence of the zones that each pastoralist follows in each year. According to the location of the campsites and the time each campsite is used by the camps, we assigned each campsites to one of the four seasons, rainy, cold dry, hot dry and transition, respectively. We plotted all campsites by season on a map (Figure 3.1) and after inspecting the map visually (i.e., if campsites in a same season are adjacent to one another, we considered that they are in a same zone), we found multiple campsite clusters for each season (three for rainy season, two for cold dry

33 season, three for hot dry season, and one transition). We then drew a 5-km buffer for each campsite to depict the potential daily grazing area. The decision to use a 5-km buffer was based on the fact that it is a good approximation to the average daily herding radius of 4.5 km obtained from the GPS tracking data (Moritz et al., 2010). Finally, we drew minimum bounding rectangles that envelop all campsites and their buffers by each cluster for each season to represent all seasonal zones. Using this procedure, we detected 9 seasonal zones in which pastoralists stay during each season (Figure 3.2).

Figure 3.2. Seasonal zones. The rectangles in green, blue, red and orange represent zones where herds stay in rainy, cold dry, hot dry and transition seasons, respectively.

Figure 3.3. Flow chart for orbit identification. Orbit 1: 2-7-8-2. Orbit 2: 1-4-8-1. Orbit 3: 1-4-7-1. Orbit 4: 3-4-8-3. Orbit 5: 3-4-6-8-9-3. Orbit 6: 3-4-6-8-3. Orbit 7: 3-4-8-9-3. Orbit 8: 3-5-4-8-3

In order to detect whether there were patterns in the seasonal transhumance movements or that all seasonal rounds were unique, we compared them to examine which seasonal rounds were similar and overlap in space and time. Analysis on the transhumance data has indicated that groups of pastoralists tend to share the same set of sequence of zones. We further identified these sequences and called each of them an orbit. To detect such orbits, we drew the movement path of each camp by sequentially connecting lines between campsites that are visited by the camp. This results in a flow chart (Figure 3.3) and we used it to identify the orbits using three criteria: (i) whether pastoralists start with other pastoralists that leave from the same rainy seasonal zone, (ii) whether pastoralists visit extreme far north areas (zone 6), and (iii) whether pastoralists

35 visit transition area (zone 9) at the end of a dry season. Because all pastoralists stay in one of the three rainy seasonal zones and move at the end of rainy season, we started the identification of the orbits by examining the rainy seasonal zone where the pastoralists stay. If there is a unique sequential zone movement, then the movement becomes an orbit. In our data, movements starting from zone 2 stand alone as a unique sequential zone movement, and we classified them as orbit 1. General movement pattern showed that most pastoralists move toward cold dry seasonal zone 4 at the end of rainy season, move toward hot dry seasonal zone 8 followed by cold dry season, and come back to their rainy seasonal zone. If some of the pastoralists move toward different cold or hot dry seasonal zone, we assigned them to different orbits. During hot dry season, some pastoralists, especially young herders, move further into northern area (zone 6) with strongest animals. These pastoralists were also assigned to different orbits. At the beginning of the rainy season, all pastoralists come back to their rainy seasonal zone and some of them visit transition area (zone 9) on their way back. Figure 3.4 shows the 8 orbits.

Once the orbits and zones were identified, we calculated the average time for the pastoralists to arrive and leave each zone for each orbit. These times provide a movement schedule that mimics the timing of the seasonal movements. For example, a pastoralist in orbit 6 will have arrival and leaving dates at days 365 and 53 (rainy season) for zone 3, days 97 and 134 (cold dry season) for zone 4, days 150 and 200 (hot dry season) for zone

6, and days 264 and 322 (hot dry season) for zone 8, where all the times are calculated using the mean arrival and leaving times of the pastoralists in this orbit. (We note that

36 day 1 refers to August 16, the starting date of our data analysis, which makes the leaving date for zone 3 smaller than the arrival date.) Each camp is represented as an agent in the model and we speculate that an agent will start to leave a zone at the specified leaving date. By leaving a zone, the agent will start to use a transhumance mode so that it stays at a location for a short amount of time (around 4 days). Between the arrival and leaving dates, the agent randomly finds a location within the corresponding zone (this random location can have any x and y coordinates within the zone) and stay there for a number of days that follows a uniform distribution between 18 and 22 days. This range is used because (1) 20 days of stay was used to identify the zones and (2) it gives certain randomness in the stays for each agent. Before the leaving date is reached, the agent continues to choose a random location and duration of stay in the zone. At the leaving date, the agent starts a directional movement toward the next zone in the orbit. The direction of the movement is determined by the angle between the current location of the agent and the center point of the next zone. A linear movement is used to guide the agent move toward the next zone. The agent stays at each location on the line for 2 to 6 days

(randomly chosen using a uniform distribution). The distance of each move on the line between two stops is randomly decided following a uniform distribution between 9 to 11 km (the average moving distance in the data is 10 km with a standard deviation of 0.7 km). Once the arrival date of the next zone is reached, the agent resumes the mode of moving randomly in the zone and staying in each location between 18 and 22 days. Using the movement described above, we can simulate the trajectory of pastoralists in each orbit

(Figure 3.5).

Figure 3.4. 8 transhumance orbits. Pastoralists move from one seasonal grazing area (box) to the next.

Figure 3.5. An example of a simulated trajectory of an agent in orbit 6. The zones in the orbits are highlighted. Each dot represents a location where the agent stays during the year of simulation and the marked number is the day of arrival. All dates start at August 16.

3.2.2 Agent-Based Disease Model

The main purpose of the agent-based model is to help us understand the impact of the seasonal movements and daily grazing activities of the mobile pastoralists on foot-and- mouth disease (FMD) transmission in the Far North Region of Cameroon. We simulate

39 the transmission of FMD among animals using an SIR model that analyzes the change of three population portions representing three critical stages of FMD: susceptible (S), infectious (I), and recovered (R). SIR models are commonly used in modeling disease transmission and there are two approaches to deriving the parameters, density-dependent and frequency-dependent (Keeling & Rohani, 2008). FMD virus transmission is usually modeled with a density-dependent approach because this approach assumes an intuitive linear relationship between the host density and the contact rate (Kao & Kiss, 2010;

Smith et al., 2009). Our model only concerns contacts between herds, we choose to use the frequency-dependent transmission approach to avoid scaling of contacts with population. To isolate the effect of herd movements on disease transmission, the disease transmission rate does not depend on herd size.

In our SIR model, we assume that the recovered individuals are immune for the whole year (Laura W Pomeroy et al., 2015). We also do not consider births and deaths in a year, because it is a relatively short epidemic time scale and thus we ignore the demographic effects on the population. As a result, the frequency-dependent SIR model calculates transitions of individuals among compartments using the following equations:

d푆 푆퐼 = −훽 d푡 푁 d퐼 푆퐼 = 훽 − 훾퐼 (1) d푡 푁 d푅 = 훾퐼 d푡

40 where S is the number of susceptible individual animals in the population, I the number of infected animals, R the number recovered animals, N the total population, β the disease transmission rate, and γ the recovery rate.

The dynamics of disease transmission depend on the basic reproduction ratio, R0, which can be described as follows:

훽 푅 = (2) 0 훾

The ratio is derived as the number of secondary cases transmitted from a single infected individual onto individuals in the susceptible population. Hence, when R0>1, an epidemic in the susceptible population will occur and the number of cases will increase.

The traditional way of simulating disease transmission using SIR models as described above may not work in a highly heterogeneous environment caused by constant movements of the population in the region. In our case, it is the seasonal movements of the pastoralists that lead to the heterogeneity. To address this issue, we first need to determine the mechanism of contact between FMD hosts. We assume that the main interaction of herds comes from sharing a common grazing area and we represent the potential grazing area of each pastoralist using a circle with a fixed radius around the its campsite. The same radius is used as a constant for the entire year. Though we have found that a 5 km grazing distance is common in area in the dry season (Moritz et al

2010), we will also test other radius values in our experiments.

To simulate FMD transmission in our agent based model, each agent has an associated number of animals in the S, I, and R stages as an attribute. Agents move based on their orbit. Within a season, agents stay at a location for around 20 ± 2 days. After 20

± 2 days, they move to a random location within the seasonal zone. At the end of the season, agents move toward the next seasonal zone. While in transit, they stay at one location for 2~6 days.

Figure 3.6. Model assumption. A black dot indicates an agent and a circle represents the potential grazing area of the agent. Red color represents infected agent and yellow indicates the agents that share the grazing area with the infected agent and are considered as a population in the SIR model. Grey represents the agents that are not considered as a population.

If an agent has at least one infected animal, which is referred as an infected agent, the infected animal can transmit the FMD virus to the susceptible animals in the same agent as well as to other agents that have contact with this agent. In our model, contact between agents are established using grazing area that each agent can possibly reach for daily grazing (pastures in our study region are in relatively flat savannah landscapes, and therefore terrain differences should not change the radius of grazing area to any large extent). For an agent that has at least one infected animal, the model searches for a cluster of agents whose grazing area overlap with the grazing area of the infected agent (see the red and yellow circles in Figure 3.6). Animals in these agents are then considered together as a fully mixed population that is then used in the SIR model.

The model proceeds in daily time steps, for 365 days. Within each time step, agents decide whether they stay at the current location or move toward the next location.

If they decide to move, then they determine the next place according to their orbits. The next step is to examine the spread of FMD virus. The model treats all infected agents and the agents that share the grazing area with infected agents as a population in the SIR model. After the completion of the SIR model, the updated values of S, I, and R for the animals are redistributed back to each agent. This process continues until the end of the simulation.

After each time step (1 day), we recalculate the S, I, and R values for each agent using the proportion of the previous values for each agent. Specifically, we have

푆 푑푆 (푡) = 푖 푑푆(푡) 푖 푆 퐼 푑퐼 (푡) = 푖 푑퐼(푡) (3) 푖 퐼 푅 푑푅 (푡) = 푖 푑푅(푡) 푖 푅 where subscript i is used to indicate the i-th agent in the model, dSi, dIi and dRi respectively are change rates of the number of susceptible, infected, and recovered, in the i-th agent, Si, Ii, and Ri respectively are the number of susceptible, infected, and recovered animals before the current day for the i-th agent, S, I, and R respectively are the total number of susceptible, infected, and recovered animals before the current day for the entire cluster, and dS and dR are calculated using the SIR model described above for the entire cluster.

3.3 Experiments

The models were used in a series of in silico experiments to demonstrate the ability of the model to capture the dynamics of FMD transmission in a setting with seasonal transhumance movements and to assess the sensitivity of the model to changes in different parameters. For these experiments, all agents are initially in the susceptible category. Though this is an endemic population, the assumption is reasonable because we have demonstrated that new FMD strains do pass through the population (Ludi et al.

2014) and that immunity does wane over time for most FMD serotypes (Laura W

Pomeroy et al., 2015). In our model, we use agents to represent camps consisting of multiple households and herds and each agent has 200 animals and the reason is that each

44 camp, represented by an agent in the model, consists of 50 to 1,000 animals with an average of about 200 animals. Because our model aims to examine seasonal and daily movements of herds and their impacts on FMD transmission, we attempt to isolate the effect of the herd size without the added stochasticity of herd size heterogeneity. By defining disease as having at least one infected animal at a given time and place, we partially control the influence of fixing herd size on our overall conclusions. Considering a different number of animals per agent should, however, not affect the epidemic pattern generated by our model. The major role that the number of animals per agent plays is that it just proportionally scales the size of infected animals per unit of time. Therefore, we suppose that including more animals per agent in our model would generate very similar dynamic epidemic pattern documented in our paper.

Each year the survey data starts on August 16, a day in the rainy season before the herders start their transhumance toward the dry season zones. We use the same date to start of simulation for the sake of consistency. The model has 67 agents and each of them represents a camp of mobile pastoralists with 200 animals. These agents are placed in the three rainy season zones: 14 in the zone 1, 4 in the zone 2, and 49 in the zone 3 (see

Figure 3.2). We initiate an FMD infection in a randomly selected animal at a random location. Because we are interested in whether the time of infection start significantly impacts FMD transmission, we designed three experiment scenarios: FMD starts on day

1 and day 31 when pastoralists are still in their rainy season zones and on day 61 when they migrate to cold dry season zones along transhumance routes where they are spatially close. Because most pastoralists stay in the Logone floodplain in the dry season and they

45 are close enough to form a fully mixing population, we exclude the uninteresting scenario that FMD starts during the dry season.

Table 3.1 summarizes the parameters used in this paper. The recovery rate (γ) varies from two to three weeks (Doel, 2005; Sanson, 1994). We use a fixed value of

0.0588 to specify a 17-day recovery process, which seems to be the average recovery value observed in the literature. We run the model with a buffer size of 1, 3, 5, and 100 km. Our choice is guided by the fact that during each day, pastoralists move their animals to nearby areas for grazing. The actual size and shape of these areas vary, but data from previous research indicates that the average daily herding radius during dry season is 4.5 km (Moritz et al., 2010). Daily herding radius is likely smaller during the rainy season than in the dry season. In the rainy season, forage available spaces are widespread and thus it is easy to obtain access to higher quality forage and water resources, whereas forage available spaces and watering points are limited in the dry season (Butt, 2010;

Turner et al., 2014). The largest buffer (100 km) represents a fully mixing population that ensures all herds are in a single SIR population throughout the entire simulation, meaning all animals in the whole Far North Region have the same contact rate with each other.

This would be reasonable if one considers unrecorded movements of animals between herds and markets, movement of humans by foot and vehicles as fomites, and other potential mechanisms of environmental transmission (Mahy, 2005).

The reproduction ratio, R0, also varies from 2.52 to infinity in the non-vaccinated cattle group (Orsel, de Jong, Bouma, Stegeman, & Dekker, 2007; Orsel, Dekker, Bouma,

Stegeman, & De Jong, 2005; Ster, Dodd, & Ferguson, 2012). To investigate wide range

46 of contagious pattern, we assume that R0 takes values 2-12. Then based on equation 2, we obtain the transmission rate range of 0.1176-0.7056. So, for our simulation we pick the following values: 0.1, 0.3, 0.5, and 0.7.

Parameter Value First day FMD introduced 1, 31 and 61 Number of agents (herds) 67 Number of animals per herd 200 Buffer size (km) 1, 3, 5, 10 and 100 Transmission rate 0.1, 0.3, 0.5 and 0.7 Recovery rate (γ) 0.0588

Table 3.1. Parameter values used in the experiments for the model

We built the agent-based model using a Java-based agent-simulation toolkit called

MASON (Luke, Cioffi-Revilla, Panait, & Sullivan, 2004). We used a circle to represent the potential area and a fixed radius for the buffers for all agents for the entire year. We changed the buffer size to explore the impact of grazing behaviors. The simulation length is one year to match the time it takes pastoralists to come back to the starting point of their orbits. For each combination of the parameters in Table 3.1, we run the model 300 times to obtain an overall distribution of infected individuals.

3.4 Results

3.4.1 Sensitivity to parameters

To quantify FMD dynamics when the outbreak was initiated at the beginning of a rainy season, we simulated our model under seasonally appropriate transhumance conditions, which means that the agents have a relatively big grazing area, so they graze farther apart from each other. Coupled with the fact that the outbreak begins at the beginning of the rainy season, the initial number of infectious animals is relatively small and reoccurs after some time when the animals reach a new small grazing area during a dry season (Figure

3.7). This causes the double peak in the distribution of infectious animals. When FMD starts in the middle of the rainy season (Figure 3.8) or during the herd transition between rainy and dry seasons (Figure 3.9), animals move to a small grazing area sooner because of a coming dry season. Consequently, the double peak in Figure 3.7 and Figure 3.8 is less pronounced (Table 3.2). Figure 3.8 depicts that many more animals get infected because they move more closely together. Thus, the single peak distribution of the infected animals is observed.

To quantify FMD dynamics based on grazing behavior, we simulated our model under grazing area sizes with a 1, 3, 5, 10 and 100 km radius. Figure 3.7 illustrates that when the grazing area is small (row 1), herds are more isolated which inhibits the disease contagion. This results in a lower epidemic peak than with bigger buffer sizes (rows 2, 3 and 4). When herds graze on a bigger area, they contact more frequently with each other and spread the FMD virus faster. This leads to a more pronounced first peak of the disease transmission (rows 2, 3 and 4 in Figure 3.7). The dynamic pattern differs much

48 more across simulations for grazing area with radius of 1km, because the FMD outbreak location matters more when agents are isolated. The bigger the grazing area, the more likely are agents to contact with each other in short period of time. As a result, a higher number of animals gets infected during the first days since the FMD outbreak. Rows 2, 3 and 4 in Figure 3.7 depict this as a higher first peak of the FMD outbreak. Compared with

Figure 3.7, Figures 3.8 and 3.9 exhibit a diminished dynamic pattern due to the fact that agents are already close to each other at the onset of FMD outbreak.

Transmission rate Scenario Buffer 0.1 0.3 0.5 0.7 1 1 0.0 100.0 99.7 99.7 3 0.0 100.0 100.0 100.0 5 0.0 100.0 100.0 100.0 10 0.0 36.3 65.7 74.7 100 0.0 0.0 0.0 0.0 2 1 0.0 90.3 100.0 100.0 3 0.0 60.0 100.0 100.0 5 0.0 49.7 100.0 100.0 10 0.0 2.3 27.0 40.7 100 0.0 0.0 0.0 0.0 3 1 0.3 19.7 77.7 98.3 3 0.0 0.3 36.7 98.0 5 0.0 0.0 40.0 74.3 10 0.0 0.0 0.0 1.7 100 0.0 0.0 0.0 0.0

Table 3.2. Percentage of simulations in which each run has more than one peak

The last row in Figures 3.7, 3.8, and 3.9 shows that a buffer of 100 km is sufficient to contain all heads in one population (e.g., fully mixing population). It represents the case of population based epidemic model. Moreover, it emphasizes that the

49 location of the FMD outbreak plays no role in this kind of model because all herds are connected throughout the entire simulation path. Therefore, all 300 runs of simulations are identical. Figures also show that for a buffer size of 10 km, 300 runs of the model for each parameter combination yield almost identical curves as for a fully mixing population under each transmission rate. The buffer size of 10 km is sufficient to allow animals enough space so that they act as if they were in one population.

For all three scenarios, the transmission rate of 0.1 appears to be too low for buffer size to play a significant role. However, for a given buffer the simulation results are very similar across transmission rates of 0.3, 0.5, and 0.7 for each considered case.

The only difference seems to be the epidemic size. We therefore note that, under our modeling setting, transmission rate does not appear to significantly change the overall

FMD dynamics, especially when the rates are greater than 0.3.

Figure 3.7. Results for the first scenario where FMD is initiated on day 1. The plot in each cell shows the results of 300 independent runs of the model using the combination of the corresponding rate and buffer size specified on the top and left of the matrix. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

Figure 3.8. Results for the second scenario where FMD is initiated on day 31. The plot in each cell shows the results of 300 independent runs of the model using the combination of the corresponding rate and buffer size specified on the top and left of the matrix. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

Figure 3.9. Results for the third scenario where FMD is initiated on day 61. The plot in each cell shows the results of 300 independent runs of the model using the combination of the corresponding rate and buffer size specified on the top and left of the matrix. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

3.4.2 Model compared to survey data

Disease incidence data were obtained by interviewing 15 mobile pastoralist herders at least twice a year (once during the rainy season and once during the dry season). The herders were asked the following question about all animals in five cattle families in their herds: “When did this animal last have FMD?” The herder reports were found to be a reliable source of information about the FMD occurrence for each animal. Maasai who are pastoralists in Kenya and Tanzania documented that the accuracy of herder diagnosis of FMD was about 73% at herd level when compared with the laboratory diagnosis

(Catley et al., 2004). We use the obtained incidence data as a point of comparison for our simulation results and to validate our model.

The simulation results show that grazing behavior represented by the radius significantly affects the dynamics of FMD. When the grazing area is 100 km, the 300 runs of the model for each parameter combination yield almost the same curves as the results using a fully mixing population under each transmission rate. Small grazing area

(≤5 km radius), on the other hand, yields different results depending on where the first

FMD infection occurs. Because of heterogeneity in agents’ mobility, our simulation results produce, on average, multiple epidemic peaks a year. Even though this contrasts the standard SIR model, which produces only one peak, our results are in line with appropriately scaled empirical evidence that we obtain from herder reports of clinical sign of disease over the last four years (Figure 3.10).

We show the percentage of simulations in which each run has more than one peak in Table 3.1. Results in this table confirm the observations from the previous figures that two peaks occur in vast majority (in more than 90% runs) of simulations under scenarios

1 and 2. However, when the disease is initiated during the animal transition path, the models generates almost no double peaks unless the transmission rate is increased to 0.5.

Figure 3.10. The number of infected animals from 2009 to 2013 based on herder reports of clinical signs of disease. We collect data from 15 herds with 50 animals in each of the herds. So for comparison purposes, each reported number of infected animals scaled appropriately since the model considers 67 mobile herds (instead of 15) and 200 animals (instead of 50).

Figure 3.11. Screen shots of the model (transmission rate =0.5, buffer size = 1km) at time step 1, 30, 90 and 120 (clockwise from top left). A dot and its circle represent an agent and its buffer, and red color indicates that the agent is infected.

Figure 3.12. Number of infected animals for each zone at each time step.

Figure 3.11 illustrates the spatial pattern of the FMD transmission among agents

(the simulation is conducted under scenario 2, with a 0.5 transmission rate and a 1km buffer size). Most agents get infected in the cold and hot dry seasonal zones. This pattern can be explained by pastoralists’ seasonal movements. Because the Logone floodplain is located in dry seasonal zones and has abundant grass during these seasons (Moritz et al.

2010), most pastoralists move toward the Logone floodplain. We believe that they contact with other pastoralists in the meantime and have a higher chance of getting infected. This situation is likely to increase the chances of transmitting the FMD virus.

For this reason, a large number of animals get infected in the cold and hot dry seasonal zones, especially, in zones 4, 7, and 8 (Figure 3.12).

3.5 Discussion and Conclusions

An important finding of this paper is that the simulation results in this paper demonstrate that after a year the FMD outbreak ceases implying that mobile herds only cannot produce a completely endemic situation. Using an agent-based model to capture the movements of mobile herds whose mobility rules are derived from a transhumance survey data, we demonstrate that a smaller grazing area allows FMD to transmit in small clusters of herds which defers the spread of the disease to other herds resulting in two epidemic peaks. This is in line with our empirical evidence that we find in herder reports.

It is clear that a sound explanation of the endemic in the Far North Region must include other factors such as the roles of sedentary and international trans-boundary herds and possible FMD carriers. We believe a more comprehensive investigation is needed, which will require a broader data collection process to allow more factors to be considered.

Our model provides an effective methodological framework to represent daily and annual movement of herds and to explore their impact on FMD transmission. By employing an ABM model, we successfully incorporate individual herd movements in the simulations and bring the model closer to the data. Starting FMD at different time points shows different dynamic patterns of FMD outbreak. The timing matters, because pastoralist seasonal movement affects the proximity of animals with respect to each other. If the FMD outbreak starts relatively early, then there are usually two peaks of the

FMD outbreak because herds are more scattered and contact with other herds is minimal.

The second peak of FMD outbreak usually diminishes when the FMD starts relatively late in the simulation because herds are close to each other as they move towards dry seasonal zones.

One of the limitations of our model is that we consider only mobile herds. We aim to relax the assumption of modeling only mobile herds in our future research and allow for sedentary herds as well. This way we think we will be able to capture the disease transmission more realistically relative to the endemic situation in Cameroon. Moreover, we plan on modeling births, deaths, and waning immunity to capture more aspects of the reality. Lastly, we assume in our model that the disease transmission rate does not depend on the herd size. However, it could be the case that the transmission rate may increase with the size of each herd. We leave this extension for future research.

Chapter 4: Describing and Explaining Patterns in Transhumance Orbits: Pastoral Mobility in the Far North Region of Cameroon

4.1 Introduction

Mobility as a fundamental means to adapt to the environment is an important characteristic in the pastoral system. Pastoralists move with their livestock to take advantage of the ecological conditions such as the accessibility of higher quality forage and water resources and minimize the damage caused by drought, diseases, and other disasters (Barﬁeld, 1993; Behnke et al., 2011; Butt, 2010; Dwyer & Istomin, 2008;

Moritz et al., 2010; D. Stenning, 1957; Turner et al., 2014). These movements have been analyzed and explained, ranging from daily grazing movement to migration depending on the spatiotemporal scales.

Specific natural, political, and social environments give rise to various forms of pastoralist movement patterns at different spatiotemporal scales (Barﬁeld, 1993). Daily grazing movements are generally loops moving between fixed points such as campsites, pastures, or watering places (Behnke et al., 2011; Moritz et al., 2010). According to the recent studies about mobility pattern analysis of livestock, the average distance that a herd travels a day during a dry season is 15 km and the average herding radius per day is 4.5 km. Night grazing has slightly different patterns compared to day grazing. At night, the herd is not watered and travels in a different direction than during the day. The

60 average distance traveled at night is 2.5 km, and the average herding radius is 0.78 km

(Moritz et al., 2010). Herd distance and herd to household radius are significantly smaller during the rainy season than in the dry season. This can be explained by forage availability. In the rainy season, forage available spaces are widespread, and thus, it is easy to obtain access to higher quality forage and water resources, whereas forage available spaces and watering points are limited in the dry season (Butt, 2010; Turner et al., 2014).

The middle-range pastoral mobility is represented by movements between two pasturelands within an ecologically unitary zone. The movement distance is between 15 and 100 km. Pastoralists stay in the area for as little as half of a month to as long as six months (Behnke et al., 2011; Moritz et al., 2010). They move even within a pastureland, mostly due to a degraded campsite by animal droppings.

Seasonal changes are derived from long-range movements of pastoralists between ecological zones where pastoralists move about 100-500 km. Seasonal migration, usually referred to as ‘transhumance’, occurs regularly according to seasonal factors (Behnke et al., 2011; D. J. Stenning, 1957). The transhumance orbits are gradually changed as a response to environmental conditions. Stenning (1957) and Bassett and Turner (2007) have described this process using the term of migratory drift.

Lastly, a movement that occurs rarely and is motivated by political or ecological factors is referred to as migration (Stenning, 1957). It occurs when a war breaks out or an infectious disease outbreak occurs, and hence, pastoralists are forced to move to an unfamiliar place. Sometimes, they have to transcend the border to avoid the crises.

This study focuses on describing and explaining pastoralists’ transhumance patterns in the Far North of Cameroon. Using a qualitative data analysis strategy and quantitative analysis method, we describe and identify the transhumance orbits. Our research team have previously used the same set of transhumance data (Xiao et al., 2015) and part of the same data (Kim, Xiao, Moritz, Garabed, & Pomeroy, 2016a). Xiao et al.

(2015) identified four transhumance modes and used them to develop a spatial-temporal mobility model. Kim et al. (2016a) identified 8 transhumance orbits by detecting seasonal grazing zones and the sequence of the zones. Even though this research successfully simulated mobile pastoralists’ movements in their agent-based disease model, one-year data does not seem to be enough to capture the overall mobility patterns of all pastoralists in the region. In this study, we use the five-year transhumance data collected through survey from 2007 to 2012.

4.2 Study Area and Data

The semi-arid climate in the Far North Region of Cameroon has four seasons: rainy, cold dry, hot dry and transition season (Moritz et al., 2013). This climate leads the spatiotemporal distributions of forage and water and as a result allows long-range movements of pastoralists between ecological zones.

For five years from 2007-2008, 2008-2009, 2009-2010, 2010-2011, and 2011-

2012, we conducted transhumance surveys to document pastoralists’ mobility in the region. The data set consists of the transhumance orbits of camp leaders (and their followers) including a unique ID for each camp leader, name of the campsite visited,

62 number of days spent in the campsite, date of arrival at the campsite, approximate location of the campsite in UTM coordinates (or decimal degrees), and ethnicity of the group. Survey data, however, is not completely reliable as it depends on pastoralists’ honesty and their memory, because pastoralists have to recall the locations (i.e. campsites) and the duration (i.e. how long they stayed in each of their locations) over the past year. For this reason, the location of campsite and timing of arrival and departing could have potential biases. Also, the total population of the mobile pastoralists in the region is not officially published so that our data could have a sampling error in terms of determining the sample size. Nevertheless, sample size (N=228) in our survey seems to be sufficient to produce reliable results. When we assume the total population size of 500 with margin of error of 5% and a confidence level of 95%, required sample size is 218.

We interviewed a total of 228 camp leaders. After initial data analysis, we excluded the data of 20 camp leaders who changed their rainy season locations and 5 camp leaders who have lots of errors such as inaccurately and incompletely reported campsite locations or dates. Given that mobile pastoralists, in general, come back to the same rainy season locations after spending the dry season, we assumed that they are in the process of changing their orbits. From 203 camp leaders, we obtained 341 transhumance orbits (128 camp leaders interviewed once, 37 camp leaders interviewed twice, 19 camp leaders interviewed three times, 13 camp leaders interviewed four times, and 6 camp leaders interviewed five times).

We used the 341 transhumance orbits to identify general spatiotemporal transhumance patterns. For the analysis of the number of camp leaders maintain same

63 pattern year by year, we included only the camp leaders who were interviewed more than one time (75 camp leaders and 213 transhumance orbits).

4.3 Methods

The goal of our analysis is to find patterns in the complex spatiotemporal data set of transhumance orbits. To identify the movement patterns of the pastoralists, we followed the next four steps.

First, we made a distinction between transit and sojourn campsites, in which the former are campsites that pastoralists use for a few days when they are on the move from one seasonal grazing area to another. Sojourn campsites are sites where pastoralists stay for a longer period, sometimes up to six months, in one seasonal grazing area. Typically, pastoralists stay for over 20 days because women generally only construct their houses when pastoralists plan to stay for more than 20 days in one place. To classify sojourn sites, we considered the sites where pastoralists stayed for over 20 days. However, this rule is not always strictly applied. Although accessibility of forage and water is a major factor to determine the movement between pasturelands, pastoralists sometime make a decision based on non-ecological factors (Behnke et al., 2011; Dwyer & Istomin, 2008;

Turner et al., 2014). Non-ecologic factors driving movement include: interest in being able to trade milk or livestock with settled population or other pastoralists, to gain better access to veterinary services for livestock, and to minimize the risk to lose their livestock during severe disease outbreaks. These non-ecological factors influence herders’ movement decisions while they move between pasturelands. Moreover, the 20-day

64 duration of sojourn sites may not be appropriate for the pastoralists who make long transhumance orbits with many movements because they do not stay for long at a campsite. For these reasons, we released the 20-day rule and considered the sites where pastoralists stayed for less than 20 days by comparing maps and Excel sheets.

Second, we identified the seasonal grazing areas based on the place names that pastoralists use. According to the climate in the region, a seasonal grazing area can be identified in the three main seasons: the rainy season (June-September), cold dry season

(October-January), and hot dry season (February-May). The problem is that many pastoralists had multiple sojourn sites both in the cold and hot dry season and that there was no clear distinction between cold and hot dry seasons. Thus, we combined the cold and hot dry seasons into a dry season and finally used two seasons: the rainy season and the dry season. We found six grazing areas in the rainy season and four grazing areas in the dry season. In order to simplify the name and ease the analysis, we assigned a letter to each place instead of using pastoralists’ toponyms (Figure 4.1).

Third, we assigned one of the two seasons to each sojourn campsite. We plotted the sojourn campsites on a map. Initially, we assigned the closest seasonal grazing area to each sojourn campsite by inspecting the map visually. We then compared the map and

Excel sheets to correct the assigned grazing season if there is a mismatch.

Fourth, we detected the sequence of the seasonal grazing areas that each pastoralist follows in each year. We used the rainy season area as the starting point of the transhumance orbit. For example, if a pastoralist starts the orbit in Fombina, stays in

65 several sojourn sites in Yaayre followed by Ndiyam Shinwa, and comes back in

Fombina, the pastoralist has the pattern B-K-M-B.

The steps outlined above allowed us to describe the patterns in transhumance orbits and classify them in different groups based on: 1) rainy season location; 2) dry season locations; and 3) sequence of the locations. Once the sequences of the visited places for all pastoralists were detected, we finally grouped them together if they have the same sequences and assumed that they have same transhumance pattern.

To examine where there are any statistical differences of characteristics among the identified orbits, we calculated the descriptive statistics for each of the identified orbits, i.e., total distance covered in one year, number of movements, distance per movement, number of sojourn sites, and duration in sojourn sites. We then ran the one- way multivariate analysis of variance (one-way MANOVA) in R 3.1.2 and considered significant at p-values < 0.05.

To see how stably camp leaders keep their orbits over time, we identified the camp leaders who have been interviewed for multiple years. We examined whether they have changed their orbits over time and described how they have changed their orbits.

Figure 4.1. Key seasonal areas

4.4 Results

4.4.1 Transhumance orbits

We identified 24 annual movement patterns. The longest distance of the average annual movement is 534.66 km, and the shortest distance of annual movement is 131.6 km

(Table 4.1). Some orbits have long annual distances (Orbits 15, 19, 16, and 22) starting from southwestern places G (Mijivin) or F (Guidiguis) and visit place L (Yaayre

Woylare), whereas other orbits have relatively short annual distances (Orbits 14, 1, 11, and 3) starting from southwestern places A (Woylare) or C (Gobogore) and spend dry season at one place near M (Ndiyam Shinwa) or K (Yaayre) (Figure 4.2). Because one of the criteria to identify the orbits is rainy season location, transhumance patterns are clearly distinguishable in accordance with rainy season location and can be classified in detail according to dry season location (Figure 4.3).

To compare visually how the orbit characteristics (total distance covered in a year, number of movements, distance per movement, number of sojourn sites, and duration in sojourn sites among orbits) vary among the identified orbits, we included the

11 identified orbits that have more than 10 camps (297 transhumance orbits, 87% of all the transhumance orbits) and drew the box plots (Figure 4.4). Relatively, the orbits that have a long total length show a higher number of movements and make short distance per movements. The number of sojourn sites is also smaller when the annual distance is short. Instead, the duration of stay in a sojourn site is longer.

With the 11 orbits, we ran the one-way MANOVA to determine if there were statistical differences among the identified orbits with the five orbit characteristics. First,

68 we checked whether there were any linear relationships among the orbit characteristics and eliminating the number of movements as a dependent variable because it had a linear relationship with the total distance covered in a year. A one-way MANOVA revealed a significant multivariate main effect on the orbits [Wilks’ λ = 0.30928, F (40, 1075) =

9.7476, p <0. 001]. Significant univariate main effects for orbits were obtained: total distance (F=37.829, p=0), distance per movement (F=5.2029, p=0), number of sojourn sites (F=2.9751, p=0.001396), and duration in sojourn sites among orbits (F=6.2712, p=0). These results indicate that the orbit characteristics distinguish pastoralists’ annual movement patterns.

Movement between Annual movement camps Orbit Num Ave. Ave. number Ave. of Visit order distance STD (km) of distance STD (km) cases (km) movements (km) 1 21 A-K-A 197.34 46.98 16.7 11.81 8.49 2 11 A-K-M-A 264.00 25.98 24.7 10.68 5.74 3 1 A-M-A 223.63 0.00 10.0 22.36 6.89 4 29 B-K-B 279.19 41.46 22.0 12.69 7.87 5 21 B-K-L-K-B 381.66 37.74 27.6 13.82 7.87 6 12 B-K-L-K-M-B 395.25 53.31 25.6 15.45 11.80 7 99 B-K-M-B 269.27 47.90 18.8 14.29 9.03 8 1 B-K-M-D-B 320.21 0.00 24.0 13.34 7.91 9 16 B-K-N-M-B 283.99 22.24 17.8 15.94 7.84 10 12 B-M-B 228.92 47.70 15.1 15.18 8.17 11 16 C-K-C 211.69 39.38 18.0 11.76 8.79 12 1 C-K-L-C 301.43 0.00 24.0 12.56 9.98 13 8 C-K-M-C 246.59 36.56 20.8 11.88 9.28 14 9 C-M-C 131.60 38.67 6.9 19.10 11.06 F-K-L-K-M-D- 15 2 534.66 59.77 36.5 14.65 8.75 F 16 3 F-K-L-K-M-F 455.62 98.77 25.0 18.22 10.18 17 7 F-K-M-F 320.88 35.52 20.1 15.93 8.38 18 1 G-K-G 304.76 0.00 20.0 15.24 6.12 19 8 G-K-L-M-D-G 497.94 43.09 34.6 14.38 8.32 20 3 G-K-M-D-G 441.04 29.27 29.7 14.87 7.98 21 34 G-K-M-G 364.53 58.48 25.0 14.58 8.60 22 1 G-L-M-G 447.38 0.00 27.0 16.57 9.88 23 1 G-M-D-G 360.67 0.00 19.0 18.98 9.84 24 24 G-M-G 257.93 61.05 15.6 16.55 9.33

Table 4.1. Descriptive statistics for orbits

Figure 4.2. 3D plots of transhumance orbits 71

Figure 4.3. Transhumance orbits in 2007-2012

Figure 4.4. Boxplots of orbit-characteristics

4.4.2 Migratory drift

With the 213 transhumance orbits from 75 camp leaders who were interviewed more than once, we investigated how many camp leaders maintain the same pattern every year. A total of 33 camp leaders out of 75 (44%) did not change their orbits, and 32 camp leaders 73 changed their orbits by adding or missing one place (Table 4.2). For example, some camp leaders made their transhumance movements following the orbit B-K-M-B in 2007-2008, but in the next year they did not visit the place K and moved following the orbit B-M-B.

The frequently changed places are the ones near the floodplain: K, M, and N. This result could be explained by the accessibility of forage and water caused by the year-to-year climate fluctuations.

Change visited place by adding or removing No change D K L M N > 2 places 33 1 7 3 13 8 10

Table 4.2. Number of pastoralists who keep or change their orbits

4.5 Discussion

A sufficient amount of samples and data allow to improve the quality and accuracy of the analysis. Controlling the various issues that can occur in the process of data collecting also affects the results of the analysis. In our transhumance survey, we could only interview 6 camp leaders, who have been in their positions for five consecutive years, even though our initial count had been 203 camp leaders. If we interviewed all pastoralists, who have held their positions for five years or longer, we would be able to describe fully how pastoralists change their orbits over time. Nevertheless, we obtained meaningful results with the data.

We eliminated, through the preliminary data analysis, the data for 25 camp leaders, who had different starting and ending places in their orbits or had include lots of

74 errors. We assumed that they were in the process of changing the rainy seasonal grazing areas and determined that it was appropriate to exclude them in the analysis. As we had examined, through a sequence alignment analysis, the rainy seasonal grazing area (i.e., starting and ending locations) has significant impact on identifying the transhumance pattern. Furthermore, we verified that each orbit has different characteristics, depending on the rainy seasonal grazing area.

Majority of the camp leaders followed the same transhumance pattern from year to year. Camp leaders, who changed their orbits, mainly changed their dry seasonal location by adding or removing place M or K. Figure 4.5 illustrates the rates of visits by camp leaders per year. The size of the symbol indicates the proportional number of camp leaders who visit the key locations in each year. The dry seasonal grazing areas, K, L, and

M, and the rainy seasonal grazing areas, B and G, have almost constant visiting rates each year although there are slight variations. These results imply that camp leaders prefer to maintain stable transhumance patterns unless there are serious social and environmental changes such as a war, drought, or epidemic disease outbreaks.

A limitation of this study is that our survey data could have potential sampling biases to represent the characteristics of the whole mobile pastoralists in the region. The sample size in our survey was, however, sufficient to produce reliable results when the total population size is 500.

Figure 4.5. Annual occupancy of grazing zones. A piece of a pie represents the percentage of visits by camp leaders a year.

4.6 Conclusion

Describing and explaining transhumance orbits allow us to develop meaningful models of pastoral mobility. Furthermore, we could use the models to predict changes in orbits by incorporating social and ecological factors that affect transhumance orbits. In this paper, we described and explained movement patterns using the analytical strategy. As a next step, we plan to use these identified patterns to examine the role of mobility in the transmission of infectious diseases.

Chapter 5: Modeling the effects of Transhumance Movement on the Transmission of Foot-and-mouth Disease

5.1 Introduction

Recent outbreaks of infectious diseases such as Ebola Virus Disease, Middle Eastern

Respiratory Syndrome, Severe Acute Respiratory Syndrome, or foot-and-mouth disease

(FMD) occur across borders and concurrently in the world. One of the most important causes of this phenomenon is widespread global trade and travel (World Health

Organization, 2007). Because the movements of individuals and goods occur globally and frequently, an infectious disease outbreak in one place can be spread throughout the world. Therefore, analyzing and predicting human and animal movements are necessary for predicting and preventing the spread of an epidemic.

Analyzing the historical epidemic data and modeling the spread of an epidemic allow us to prepare for new epidemics in the near future and can also be the basis of a policy decision. Many researchers have been involved in modeling different infectious diseases (Lessler et al., 2014; Tildesley, Smith, & Keeling, 2009; Wesolowski et al.,

2015). Recent literature has shown different approaches by incorporating individual movement and heterogeneity for infectious disease (Kao, 2003; Tildesley et al., 2009). In our previous research (Kim et al., 2016a), we modeled daily and annual movement of mobile pastoralists in the Far North Region of Cameroon and examined their impact on

FMD transmission. Even though we successfully simulated individual herd movements and spread of FMD, the model was limited to represent different types of herds and ignored demographic consideration or waning immunity to capture more aspects of the reality.

In this study, we model the effects of the transhumance movements of mobile pastoralists in the Far North Region of Cameroon on FMD transmission to investigate and understand more comprehensively than the previous model. To address two main questions: 1) how do the movement patterns of mobile pastoralists impact on FMD transmission, and 2) what would have happened if there is a change in the regular transhumance movements, we develop an extended agent-based simulation of FMD in the region. We include sedentary herds in addition to mobile herds to overcome the limitations that the previous model has and provide a more realistic representation of the region and mobility patterns. We also consider births, deaths, and waning immunity in the population. We design seven experimental scenarios to evaluate the impacts of mobile pastoralists’ regular movements and changes in the movement patterns on the

FMD epidemic.

5.2 Background information on study area

The Far North Region of Cameroon has a mobile pastoral system that allows mobile pastoralists make long-range movements between ecological zones (Moritz et al., 2010).

Because the region has a semi-arid climate including rainy and dry season and these climate changes during a year alter the spatiotemporal distributions of forage and water,

78 mobile pastoralists move with their livestock between rainy season and dry season pastures to maximize grazing (Moritz et al., 2013).

Almost all countries of sub-Saharan Africa where pastoral systems predominate have experienced endemic FMD (Vosloo et al., 2002). The Far North Region of

Cameroon is also in an endemic or repeated epidemic situation of FMD with most outbreaks caused by serotypes A and O in cattle (Ekue et al., 1990; Vosloo et al., 2002).

Due to inadequacy or lack of disease surveillance systems, outbreaks are not properly reported and/or documented in these regions.

FMD virus can be transmitted by aerosol, by carrying on clothes or shoes of people that have had contact with infected animals and vehicles that have visited infected farms or animals eating virus contaminated products (Mahy, 2005). One of the most likely ways to spread the virus is the movement of infected animals. The mobile pastoral system in the Far North Region of Cameroon and daily grazing behavior allow the frequent contact among herds. For this reason, mobile herds may play a significant role in the dynamics of FMD transmission.

Figure 5.1. The Far North Region of Cameroon

5.3 Design of agent-based model

Despite the fact that our previous research and model investigated daily and seasonal movements of mobile pastoralists and their impacts on FMD transmission in the Far

North Region of Cameroon, a more comprehensive investigation is needed to understand how the mobile pastoralists’ movements influence the epidemic pattern in the long-term under an environmental setting with sedentary herds. How do the movement patterns of

80 mobile pastoralists impact on FMD transmission? What would have happened if a seasonal area had been inaccessible due to a social or environmental issue, and hence, seasonal movement patterns of mobile pastoralists had changed? Also, how do the changes in population density in a seasonal grazing area affect the epidemic patterns? To better address these questions, we developed an extended agent-based simulation of FMD in the Far North Region of Cameroon including mobile pastoralists and sedentary herds.

The new agent-based model builds upon and extends based on our previous research

(Kim et al., 2016a; Kim, Xiao, Moritz, Garabed, & Pomeroy, 2016b).

5.3.1 Landscape

The model landscape is 200 km by 200 km, which is simplified based on the Far North

Region of Cameroon, which is approximately 240 km from east to west and 270 km from north to south. The original landscape is presented in Figure 5.1. In the orbit analysis in

Chapter 4, we identified six rainy season locations and four dry season locations. Even though the 10 seasonal locations are important to describe and explain the whole patterns of transhumance movements in the region, some places are visited by only a few mobile pastoralists. Thus, we assumed that their movements have a relative lack of influence on disease transmission. In the model landscape, we combined two locations, G and F, into one seasonal area because these two areas are relatively small, and transhumance orbits that start from these locations make similar patterns. We also ignored locations D and N.

According to the orbit analysis, a small number of camps visit D at the end of the dry season for a few days before they come back to their rainy seasonal pasture, and only one

81 orbit visits the N area. Finally, the landscape consists of seven seasonal areas (four rainy and three dry season areas) and two different sedentary livestock density areas. Each A K L seasonal area is a square, measuring 30 km each side, and is placed in a position that approximates the relative geographic distance from one another (Figure 5.2).

B M A K L

Low livestock densities

CB MD A K L

Low livestock densities High livestock densities

BC MDE (G+F) Low livestock densities High livestock densities

Figure 5.2. The landscape of the model. The green rectangles represent rainy season areas, and the yellow rectangles represent dry season areas. The arrows indicate the direction of the mobile agents’ movements. C D

5.3.2 Agents High livestock densities

Agents are divided into two types: sedentary agents and mobile agents. A sedentary agent represents a village, and a mobile agent represents a camp that consists of several mobile pastoralists. Through an image analysis of the village distribution in the region, we identified approximately 20,000 villages that may or may not have cattle. Also, there are

292 mobile pastoralists who were interviewed in our transhumance survey for five years, from 2007 to 2012. For this model, we used 5,000 sedentary agents and 500 mobile agents, and each sedentary and mobile agent consists of 100 and 500 animals, respectively (Moritz, Hamilton, Scholte, & Chen, 2014).

At the beginning of the simulation, the model generates the two types of agents and assigns their locations, number of animals, and orbits for mobile agents. Sedentary agents are randomly distributed at a ratio of 2 to 8 in the low and high livestock density areas, respectively. The mobile agents are randomly distributed within the rainy season areas corresponding to their orbits. An agent interacts with neighboring agents and infects or is infected by others. As a result of the interaction, the model updates the number of animals of each agent belonging to one of the epidemic stages: susceptible, infected, and recovered.

5.3.3 Mobility rules

We designed the mobility functions for mobile agents based on our transhumance survey data and the mobility patterns of mobile pastoralists in the Far North Region of

Cameroon (Kim et al., 2016a; Moritz et al., 2013; Moritz, 2010; Xiao et al., 2015).

According to the analysis on the transhumance data in Chapter 4, mobile pastoralists tend to follow the same set of sequence of seasonal areas. We identified these sequences, called orbits. Among the 24 identified orbits, we eliminated the orbits that have the removed locations in the section 5.3.1, and selected 10 representative orbits that about 90

% of pastoralists follows (Table 5.1). To decide the number of agents for each orbit, we

83 first brought the numbers from the orbit analysis and recalculated them. Because the number of agents is related to the epidemic size and pattern, we adjusted the numbers to be evenly distributed in the four rainy season areas: A, B, C, and E have 125 mobile agents, respectively. Finally, all the rainy season areas have the same density of mobile agents. We then calculated the mean arrival and leaving times of the pastoralists and the standard deviations for all seasonal areas in each orbit. Using the calculated values, the model assigns movement schedules that follow normal distributions of the mean arrival and leaving dates for each seasonal area to mobile agents. Thus, the agents who follow the same orbit have slightly different movement schedules.

Number Mean arrival and Orbit Path STD of agents leaving times 1 A-K-A 70 (0,46) (98,296) (345,365) (0,7) (21,31) (12,0) (0,46) (112,190) (234,296) (0,7) (31,18) (50,45) 2 A-K-M-A 55 (331,365) (11,0) 3 B-K-B 25 (0,47) (102,297) (331,365) (0,8) (15,33) (19,0) (0,61) (99,180) (232,300) (0,10) (48,21) 4 B-K-M-B 75 (349,365) (41,34) (18,0) 5 B-M-B 25 (0,79) (98,295) (341,365) (0,8) (30,36) (9,0) 6 C-K-C 55 (0,51) (109,300) (347,365) (0,12) (28,23) (12,0) (0,49) (88,215) (235,288) (0,14) (60,32) 7 C-K-M-C 35 (345,365) (44,36) (7,0) 8 C-M-C 35 (0,50) (92,299) (348,365) (0,11) (53,27) (14,0) (0,50) (103,191) (230,303) (0,11) (25,26) 9 E-B-K-M-E 80 (351,365) (39,35) (11,0) (0,10) (17,18) (0,64) (108,173) (191,222) 10 E-B-K-L-M-E 45 (34,17) (21,27) (262,300) (353,365) (10,0)

Table 5.1. Orbits for mobile agents. The letters in each path are associated with the seasonal areas in Figure 5.2. Each mobile agent follows one of the orbits and repeats the orbit every year. The numbers in a parenthesis represent the mean arrival and leaving dates and their standard deviations corresponding to the seasonal area. The agents who follow orbit 9 or 10 pass through area B but do not stay in the area.

When a mobile agent is in a season (i.e., between the arrival and leaving dates), the agent randomly chooses a location in the corresponding seasonal area, stays there for at least 20 days or up to three months and continues to find a random location before the leaving date is reached. On the leaving date, the agent moves toward the next seasonal area in the orbit. In between the current and next seasonal areas, the agent makes a linear movement within the daily distance range between 9 to 11km that follows a uniform distribution and stays at the location for 2 to 6 days.

5.3.4 Epidemic rules

The epidemic follows a susceptible-infected-recovered (SIR) model with waning immunity. This model assumes that an infected individual moves from a susceptible to an infected state and infects other individuals. After a period of time, the individual finally recovers. Because we have run the model for multiple years, we assumed that immunity lasts for a limited period, and the recovered individuals move to the susceptible state

(Laura W Pomeroy et al., 2015). We also considered births and deaths in a year. As a result, we use the following equations (Keeling & Rohani, 2008): d푆 = 휇 + 휔푅 − 훽푆퐼 − 휇푆 d푡 d퐼 = 훽푆퐼 − 훾퐼 − 휇퐼 (1) d푡 d푅 = 훾퐼 − 휔푅 − 휇푅 d푡

where S is the number of susceptible individual animals in the population, I the number of infected animals, R the number recovered animals, μ the birth and death rate, ω the 85 immunity rate, β the disease transmission rate, and γ the recovery rate. The disease transmission rate depends on the basic reproduction ratio, R0 = β/(γ +μ).

A susceptible animal in an agent can become infected if the agent has at least one infected animal or when the agent comes into contact with an agent who has an infected animal. (We assumed that two agents come into contact when their potential daily grazing areas are overlapped.)

At every time step, the models run the epidemic model. Because the model considers the infected agent and the agents that share the potential daily grazing area with the infected agent as a population in the epidemic model, the size of the total population changes at each time step. Once the epidemic model is completed, the updated number of animals in each disease state is redistributed back to each agent based on the equation (2):

푆 푑푆 (푡) = 푖 푑푆(푡) 푖 푆 퐼 푑퐼 (푡) = 푖 푑퐼(푡) (2) 푖 퐼 푅 푑푅 (푡) = 푖 푑푅(푡) 푖 푅 where subscript i is used to indicate the i-th agent in the model; dSi, dIi, and dRi respectively are change rates of the number of susceptible, infected, and recovered, in the i-th agent; Si, Ii, and Ri respectively are the number of susceptible, infected, and recovered animals before the current day for the i-th agent; S, I, and R respectively are the total number of susceptible, infected, and recovered animals before the current day for the entire cluster; and dS and dR are calculated using the SIR model described above for the entire cluster.

5.3.5 Model parameters

We selected the parameter values for the simulations based on the transhumance survey and epidemiological data and literature (Table 5.2). We commenced the simulation on

August 16 which is the starting day of the survey each year and a day in the rainy season before mobile pastoralists start their transhumance. We also initiated an FMD infection on the same day.

The average daily grazing radius during the dry season is 4.5 km and is likely smaller during the rainy season (Moritz et al., 2010). We chose 1, 5, and 10 km to evaluate the effects of the agents’ daily movements on the epidemic pattern at the minimum, mean and maximum levels. We set the probability of birth and death at

0.000136 which is derived from the incidence data of the region.

The epidemic parameter values vary depending on the species of livestock and the strain of the virus. The period of immunity of FMD serotypes in the region ranges from

0.5 years to lifelong (Laura W Pomeroy et al., 2015). Because serotype O is the highest prevalence in Cameroon (Ludi et al., 2014), we used an immunity duration of 3.8 years for serotype O (Laura W Pomeroy et al., 2015). We used a fixed recovery rate of 17 days which seems to be the average value from two to three weeks (Doel, 2005; Sanson,

1994). We also set the basic reproduction ratio at 10 to investigate the wide range of contagious pattern from a large range from 2.52 to infinity depending on the population and epidemic setting (Orsel, Dekker, Bouma, Stegeman, & Jong, 2005; Orsel, Jong,

Bouma, Stegeman, & Dekker, 2007; Ster et al., 2012).

Parameter Value Number of sedentary agents 5,000 Number of mobile agents 500 Number of animals per sedentary agent 100 Number of animals per mobile herd 500 Potential daily grazing area (km) 1, 5, and 10 First day FMD introduced 1 Birth and death rate (μ) 0.0001 day-1 Immunity rate (ω) 3.8 years-1 Recovery rate (γ) 17 days-1

Reproduction ratio (R0) 10

Table 5.2. Parameter values used in model simulations

5.4 Experiments

We built the agent-based model using a Java-based agent-simulation toolkit called

MASON (Luke et al., 2004). To evaluate movement impacts of mobile agents on the disease epidemic, we designed different scenarios as below:

Scenario 1: The model includes only mobile agents. Each mobile agent moves

based on the assigned orbit. The world includes all the rainy and dry season areas.

Scenario 2: Model includes only sedentary agents. The world includes all the

rainy and dry season areas.

Scenario 3: The model includes sedentary agents and mobile agents. Each mobile

agent moves based on the assigned orbit. The world includes all the rainy and dry

season areas.

Scenario 4: The model includes sedentary agents and mobile agents but the

mobile agents do not move for the entire simulation (i.e., the mobile agents are

considered as sedentary agents). The world includes all the rainy and dry season

areas.

Scenario 5: The model includes sedentary agents and mobile agents. One rainy

season area is removed (D in Figure 5.2). The mobile agents starting their orbits

in the removed rainy season area do not move and are considered as sedentary

agents.

Scenario 6: The model includes sedentary agents and mobile agents. One dry

season area is removed (M in Figure 5.2). The mobile agents’ behaviors are

different in the sub-scenarios: (1) Scenario 6-1: the mobile agents visiting the

removed dry season area do not move and are considered as sedentary agents; (1)

Scenario 6-2: the mobile agents visiting the removed dry season area change their

orbits and visit K or L during the dry season instead of M.

Scenario 7: The model includes sedentary agents and mobile agents. Mobile

agents do not have assigned orbits and move based on random walk hypotheses

(Spitzer, 2013).

For all the scenarios, except scenario 1, the disease starts at the beginning of the simulation in a randomly selected sedentary agent within the shaded area in Figure 5.2.

Because scenario 1 includes only mobile agents and evaluates their impacts on the disease, FMD starts in the nearest mobile agent from the shaded area. The model

89 proceeds in daily time steps and runs for 5 years. To obtain an overall distribution of infected individuals, we ran the model 100 times for each scenario. We decided 100 times are sufficient for reliable results (Figure B.1).

5.5 Results

We ran the model to investigate how mobile agents’ movements affect epidemic patterns and what happens if a change in their regular movement patterns occurs.

5.5.1 Movement effects on the epidemic patterns

In our previous research, we identified that mobile pastoralists only cannot maintain a completely endemic situation (Kim et al., 2016a). We designed the previous model to run for a year, assumed that the recovered animals were immune for the whole year, and ignored the demographic effect. Because we designed the model under different assumptions in this research, we observed slightly different results (Figure 5.4). Mobile agents with a 1 km grazing area show a tendency to decrease the epidemic, but the ones with 5 or 10 km grazing areas produce increasing epidemic patterns after about three years, which corresponds to the period of waning immunity.

Simulations without movements (scenario 2 and scenario 4) produced relatively small epidemic sizes because only neighboring agents of the FMD initiated agent could get infected (Figure5.3). Each run of simulations had almost identical epidemic patterns, and only epidemic sizes were different (Figure 5.5 and 5.7).

Figure 5.6 illustrates that the epidemic patterns together with mobile agents and sedentary agents (scenario 3) are similar to the one with mobile agents only (scenario 1).

Because the mobile agents infect neighboring sedentary agents, their movements affect the epidemic size. However, it is possible that there are no movement effects when the grazing size is 1 km (row 1 in Figure 5.6). Because the outbreak starts in one of the sedentary agents and there is a lower probability that the infected sedentary agent shares the grazing area with others, there could be no epidemic or very small epidemic.

For all the scenarios, simulations with large grazing sizes (5 and 10 km) were associated with the more rapid spread of the epidemic. This is because of more opportunities for agents to interact and to carry the FMD virus to one another. In contrast, a small grazing size (1 km) limits the agents’ interactions and the likelihood that the

FMD virus reaches them.

Figure 5.3. Maximum number of infected animals (top) and peak time of epidemic curve per scenario (bottom).

Figure 5.4. Results for the first scenario. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

Figure 5.5. Results for the second scenario. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

Figure 5.6. Results for the third scenario. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

Figure 5.7. Results for the fourth scenario. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

5.5.2 Effects of changing movement patterns

To investigate the changes in movement patterns of mobile agents and the impacts on epidemic patterns, we removed a seasonal area and changed the movement patterns of the mobile agents who visit the seasonal area. The mobile agents, who spend the rainy season in the removed rainy season area for scenario 5, make the longest transhumance movements and are the only ones who visit the dry season area L. Compared with scenario 3, the limits of their movements decrease the epidemic size but do not significantly affect the overall epidemic patterns with the grazing sizes of 5 and 10 km

(Figure 5.3 and 5.8). Simulations with grazing size 1 km produce the continued growth of the epidemic.

We simulated two scenarios for the changes in mobile agents when a dry season area is removed. When the mobile agents visiting the removed dry season area do not move and are considered as sedentary agents, the epidemic sizes significantly decrease, especially with 1 and 5 km grazing areas (Figure 5.3 and 5.9). On the other hand, when mobile agents change their orbits and visit K or L during the dry season instead of M, the epidemic sizes do not show a significant difference compared to the scenario 3. Rather the epidemic sizes with grazing area 1and 5 km increase (Figure 5.3 and 5.10). 70 % of the mobile agents visit the dry season area M. Their movement restrictions or changes cause different probabilities to come into contact with mobile agents and between mobile and sedentary agents. The results exert influence on the epidemic size.

Lastly, we assumed that mobile agents do not have designated orbits and move randomly. Because they can go wherever they want even if the location is not the

97 seasonal area, they infect almost every agents in a very short time, especially with 5 and

10 km grazing area (Figure 5.11). The epidemic speed when the grazing area is 1 km is very slow but the epidemic size seems to increase over time.

Figure 5.8. Results for the fifth scenario. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

Figure 5.9. Results for the sixth scenario where the mobile agents starting the orbits in the removed rainy season area do not move. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

100

Figure 5.10. Results for the sixth scenario where the mobile agents starting the orbits in the removed rainy season area change their orbits. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

101

Figure 5.11. Results for the seventh scenario. The plot in each cell shows the results of 100 independent runs of the model corresponding buffer size specified on the left of the plots. The red line represents the mean output of the simulations. The vertical axis of each plot shows the number of infectious animals.

102

5.5.3 Relationship between population density in seasonal areas and epidemic size

Depending on the mobile agents’ movements, population densities in a seasonal grazing area vary each time. Because we designed each rainy season area with the same number of mobile agents, population densities are even for all the rainy season areas.

Each dry season area, however, has different population densities. Figure 5.12 illustrates the number of agents for each dry season area and the number of infected animals for four scenarios that have different mobile agents’ movement patterns. Whether or not visiting the dry season areas of mobile agents has a significant impact on the epidemic size, when the mobile agents’ movements are limited due to the enclosed seasonal areas

(scenario 5 and 6-1), the peak of epidemic decreases. Changes in orbits, i.e., visiting other dry season areas instead of the specified one in the orbit (scenario 6-2), however, do not significantly affect the epidemic pattern.

Figure 5.12. Relationship between population densities in dry season areas and epidemic sizes. The lines in the plots represent the mean number of agents in each dry season areas and the mean number of infected animals for each scenario. 103

5.6 Model comparison and validation

To evaluate the model, we compared the simulation results with survey data and the results from the previous model.

5.6.1 Comparison of the simulated epidemics with survey data

We obtained disease incidence data by interviewing 15 sedentary and 15 mobile pastoralist herders at least twice a year (once during the rainy season and once during the dry season). Although these surveys are based on herder reports, herder diagnosis of

FMD provides a reliable accuracy when compared with the laboratory diagnosis (Catley et al., 2004).

Figure 5.13 shows empirical evidence that we obtained from herder reports of clinical sign of disease over the last three years. Mostly, the outbreaks have repeatedly occurred during the dry season. Our simulation results, on the other hand, show a trend of increasing prevalence about three to four years after the first outbreak. These results can be explained in terms of the model assumption for FMD transmission. We considered only one virus strain (Type O) and ignored the possibility that multiple strains can be circulating simultaneously. Previous studies on FMD transmission in the region underpin our results by analyzing serology data revealing that animals showed serological reactions against multiple serotypes (Ludi et al., 2014) and that the waning seropositivity of type O lasts for approximately four years (Laura W Pomeroy et al., 2015).

104

Figure 5.13. The percentage of infected animals from 2010 to 2013 based on herder reports of clinical signs of disease

5.6.2 Comparison of the simulated results with previous model

In the first scenario, the model includes only mobile agents, which is the same setting as the previous model in Chapter 3. The simulation results from the previous model

(Figure 3.7), however, show epidemic patterns different from the results of the current model (Figure 5.4). The differences between the two models are the model landscapes and resultant movement patterns, as well as epidemiological assumptions. To investigate which one leads to the different results, we applied the orbits used in the current model to the previous model and simulated the FMD transmission. In both simulations, the results demonstrate that the incidence of FMD after a year has disappeared. This conflicts with the results from scenario 1 where the FMD incidence shows a tendency to decrease, but, after about three years, increase pattern. This result implies that epidemiological assumptions regarding contact structure within the population make a big difference in terms of epidemic patterns. Even though the general epidemic patterns in both scenarios

105 are similar, the number of epidemic peaks and the timing of the peaks are slightly different. The previous model with the eight orbits produces the highest peak first followed by smaller peaks, whereas the model with the new landscape and the ten orbits yields the opposite situation. This indicates that spatial variation and the consequential differences in movement patterns lead the differences of the epidemic pattern.

Figure 5.14. Comparison of the simulation results. The left plots show the results from the previous model with the eight orbits and the right plots the results from the previous model with the new landscape and the ten orbits.

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5.7 Discussion

The simulations with various scenarios for different movement patterns have provided a valuable opportunity to better understand the movement effects and epidemic patterns in the Far North Region of Cameroon. Our model has allowed different types of herds and their daily and seasonal movements and has provided insights into the mobile pastoralists’ movements that have influenced the spread of FMD.

By applying mobile agents’ movement rules derived from the transhumance survey and disease parameters calculated from the historical FMD incidence data of the region, we have successfully explored the movement impacts on FMD transmission. The changes in mobile pastoralists’ movement patterns from their regular ones that could have happened due to a social or environmental issue allowed different epidemic patterns such as bigger or smaller epidemic size and earlier or later epidemic peak. The changes in total population densities of mobile pastoralists in the dry season areas affect the epidemic size, but changes in the population in a specific dry area was not significantly related.

Epidemiological assumptions regarding contact structure within the population

(i.e., frequency-dependent and density-dependent transmission) lead different results in terms of epidemic patterns. In this study, we applied the density-dependent transmission that assumes contact per unit time per individual increases linearly with the population size (Keeling & Rohani, 2008). This assumption could affect the epidemic patterns with changing in the population size, especially for the scenario 1 that has different numbers of agents with other scenarios.

107

Our model has consisted of sedentary and mobile herds and did not include transboundary herds. We have considered only one type of strain that circulates in the region. The simulation results produced a longer cycle term of prevalence compared to the empirical data that shows the outbreak occurs repeatedly each year, especially during the dry season. By incorporating international transboundary herds and different types of strains, we may capture more aspects of reality.

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Chapter 6: Conclusion

6.1 Summary

The movements of individuals are closely related to the spread of a disease. By sharing space and time, individuals can come in contact with others, which enables the infectious disease to spread. Thus, analyzing and predicting the individuals’ movements allow us to predict the future outbreak patterns of infectious diseases easily and to minimize the risk caused by the outbreak. This dissertation analyzes mobile pastoralists’ movements and their impacts on FMD transmission in the Far North Region of Cameroon.

First, this dissertation reviews extensive current research related to the topic including human and animal mobility pattern analysis, modeling human behavior, modeling epidemic process, agent-based modeling, and FMD in Chapter 2. Through literature review, we broadly understand previous research and realize the needs of research on individual movements and their impacts on disease transmission.

Chapter 3 models the impact of the movements of mobile pastoralists on foot-and- mouth disease (FMD) transmission in a transhumance system in the Far North Region of

Cameroon. We first analyze transhumance data to derive mobility rules that can be used to simulate the movements of the agents in the model. We develop an agent-based model coupled with a SIR model. Each agent represents a camp of mobile pastoralists with multiple herds and households. The simulation results demonstrate that the herd mobility 109 significantly influenced the dynamics of FMD. When the grazing area is not explicitly considered (by setting the buffer size to 100 km), all the model simulations suggest the same curves as the results using a fully mixing population. Simulations that used grazing areas observed in the field (≤5 km radius) result in multiple epidemic peaks in a year, which is similar to the empirical evidence that we obtained by surveying herders from our study area over the last four years.

Chapter 4 describes and explains pastoralists’ mobility patterns using data collected over a five-year period. Using a qualitative data analysis strategy and quantitative analysis method, we identify 24 transhumance orbits and reveal that majority of the camp leaders follow the same orbits of previous years. This implies that camp leaders prefer to maintain stable transhumance patterns unless there are serious social and environmental changes such as a war, drought, or epidemic disease outbreaks. With the identified orbits, we propose behavioral parameters for animal/herd movement rules that are used for the mobility rules for agents in Chapter 5.

Finally, Chapter 5 develops an extended agent-based simulation model of the model we developed in Chapter 3 by including not only the mobile pastoralists but also the sedentary herds in the region and considering births, deaths, and waning immunity in the population. By simulating with various scenarios designed to evaluate the impacts of mobile pastoralists’ regular movements and changes in the movement patterns on the

FMD epidemic, this model provides a valuable opportunity to better understand the movement effects and epidemic patterns in the region. By comparing the simulation results from the previous model developed in Chapter 3, we demonstrate that spatial

110 variation and the consequential differences in movement patterns lead the differences of the epidemic pattern.

In sum, by employing an agent-based approach, we successfully implement individual heterogeneity into our models and explore the impact of human and animal movements on disease transmission. The dissertation research contributes in two aspects.

First, the analytical strategy to describe and explain pastoralists’ mobility patterns will make it possible to predict changes in orbits. Second, the models we developed in this research will provide a tool to test control strategies to halt FMD transmission in the Far

North of Cameroon. Such a tool could also be developed for other endemic locations with mobile populations.

6.2 Future Research

The model developed in this dissertation research consists of sedentary and mobile herds, and does not include transboundary herds. We also assumed that only one type of strain of FMD virus circulates in the region. To evaluate and predict the real world situation by simulating the model, we need to incorporate all types of herds in the region and different types of strains to the model.

Lastly, this dissertation research can extend by further validating the model and simulation results with laboratory-confirmed disease data in the Far North Region of

Cameroon. Currently, we have validated the simulation results with the incidence data that we obtained by interviewing the mobile and the sedentary herders in the region. Even though the herder diagnosis of FMD provides a reliable source of information comparing

111 with the laboratory diagnosis (Catley et al., 2004), we will better evaluate our model with laboratory-confirmed disease data. In addition, the data will allow us to derive the disease parameters to fit the model to the epidemic situation in the region.

112

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Appendix A: ODD protocol for the model in Chapter 3

We build the model in the MASON toolkit, which is a Java-based agent-simulation library (Luke et al., 2004). We have described our model here following the Overview,

Design concepts, and Details (ODD) protocol (V. Grimm et al., 2010; Volker Grimm et al., 2006).

OVERVIEW

Purpose. The purpose of the model is to understand how host mobility affects disease transmission. More specifically, we examine the impact of seasonal movements and daily grazing activities of mobile pastoralists on the transmission of foot-and-mouth disease

(FMD) in the Far North Region of Cameroon.

State variables, and scales.

Mobile pastoralist: The agents represent mobile pastoralists that have herds consisting of

200 animals. The risk of disease transmission increases when agents are in close proximity, for example when sharing common grazing areas or transhumance routes. To represent the risk of transmission due to proximity we use a buffer with a fixed radius for all agents for the entire year. We change the buffer size to explore different scenarios of

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the geographic extent of contact among agents through unrecorded animal movements,

shared grazing areas, human movements, and possible environmental transmission.

Each agent has an associated number of cattle in the S, I, and R states. As an attribute. If

an agent has at least one infected animal, it can transmit the FMD virus not only to the

cattle in the same agent but also to other agents. Table 1 summarizes the parameters used

in the study.

Agents move based on their orbit (see Figure 3.4). Within a season, herds stay at a

location for around 20 ± 2 days. After 20 ± 2 days, they move to a random location

within the seasonal zone. At the end of the season, agents move toward the next seasonal

zone. While in transit, they stay at one location for 2~6 days.

Spatial and temporal scales: The landscape for the model is 200 km by 200km. There are

9 seasonal zones: three rainy, two cold dry, three hot dry and one transition season (see

Figure 3.3). One time step in the model is a day. Each simulation runs for 365 days.

Process overview and scheduling. The model proceeds in daily time steps. Within each

time step, agents decide whether they stay at the current location or move toward the next

location. If they decide to move, then they determine the next place according to their

orbits. The next step is to examine the spread of FMD virus. The model investigates all

infected agents and the agents that are within the buffer of infected agents or have buffers

that overlap the buffers of infected agents – neighboring agents. All neighboring agents to

infected agents are set as an initial population in the SIR model. The SIR model is run for

one time step. After completion of SIR model, the updated values of S, I, and R for the

124 cattle are redistributed back to each agent. This process continues until the end of the simulation. The model process is presented in the following pseudo code.

INITIALIZATION Set user defined parameters Create agent world and seasonal zones Create orbits for agents Place the agents in the rainy seasonal zones

EACH TIME STEP Each agent: If the time step is in the rainy or dry season If the agent stays at a location more than 20±2 days then Moves to a random location within the seasonal zone End if Else If the agent stays at a location more than 4±2 days then Moves toward the next seasonal zone End if

Set up population groups For 1 to the total number of agents If an agent has at least one infected animal and has not been assigned to any population group then Assign this agent to a new population group Investigate the agents that neighbor this agent Assign the agents to the same population group with this agent End if Next agent

For 1 to the total number of population group Run SIR model Redistribute the updated values of S, I and R to each agent (as specified in Equation 3) Next population group Store the values of S, I and R for each agent

DESIGN CONCEPTS

Emergence. Spatiotemporal dynamics of foot-and-mouth disease epidemics emerge from daily and seasonal movements of herds and the transmission of the disease.

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Stochasticity. At the beginning of the simulation, all agents are randomly distributed in the rainy season zones. Although they migrate along their annual orbits, their specific locations within each zone and in transit are decided randomly because the orbits have only seasonal zone order. In addition, FMD virus is started in a randomly selected animal.

Interaction. Interactions among agents are through shared space and the FMD virus is transmitted from infected animals to susceptible animals.

Observation. The total number of individuals in each compartment (S, I and R) is collected at every time step.

DETAILS

Initialization. All agents are initially in the susceptible category. The starting day of the model is always August 16, to be consistent with the survey data. The location at which

FMD outbreak starts is randomly selected. We design three experiment scenarios: FMD starts at day 1 and day 31 when pastoralists are still in their rainy season zones and at day

61 when they migrate to cold dry season zones along transhumance routes where agents are spatially close.

Input data. To assign the movement rule to each agent, we import 8 different orbits and 9 seasonal zones that we identified from transhumance survey data.

Submodels.

Movement model: Between the arrival and leaving dates, an agent randomly finds a location within the corresponding zone (this random location can have any x and y

126 coordinates within the zone) and stay there for a number of days that follows a uniform distribution between 18 and 22 days. This range is used because (1) 20 days of stay was used to identify the zones and (2) it gives certain randomness in the stays for each agent.

Before the leaving date is reached, the agent continues to choose a random location and duration of stay in the zone. At the leaving date, the agent starts a directional movement toward the next zone in the orbit. The direction of the movement is determined by the angle between the current location of the agent and the center point of the next zone. A linear movement is used to guide the agent move toward the next zone. The agent stays at each location on the line for 2 to 6 days (randomly chosen using a uniform distribution).

The distance of each move on the line between two stops is randomly decided following a uniform distribution between 9 to 11 km (the average moving distance in the data is 10 km with a standard deviation of 0.7 km). Once the arrival date of the next zone is reached, the agent resumes the mode of moving randomly in the zone and staying in each location between 18 and 22 days.

Disease model: To simulate the transmission of FMD among agents, we use an SIR model that analyzes the change of three population portions representing three critical stages of FMD: susceptible (S), infectious (I), and recovered (R). In our SIR model, we assume that the recovered individuals are immune for the whole year. We also do not consider births and deaths in a year, because it is a relatively short epidemic time scale and thus we ignore the demographic effects on the population. As a result, the frequency- dependent SIR model calculates transitions of individuals among compartments using the following equations:

127 d푆 푆퐼 = −훽 d푡 푁 d퐼 푆퐼 = 훽 − 훾퐼 (1) d푡 푁 d푅 = 훾퐼 d푡 where S is the number of susceptible individual animals in the population, I the number of infected animals, R the number recovered animals, N the total population, β the disease transmission rate, and γ the recovery rate.

The model treats all infected agents and their neighbors as a population in the SIR model.

After the completion of the SIR model, the updated values of S, I, and R for the cattle are redistributed back to each agent. This process continues until the end of the simulation.

After each time step (1 day), we recalculate the S, I, and R values for each agent using the proportion of the previous values for each agent. Specifically, we have

푆 푑푆 (푡) = 푖 푑푆(푡) 푖 푆 퐼 푑퐼 (푡) = 푖 푑퐼(푡) (2) 푖 퐼 푅 푑푅 (푡) = 푖 푑푅(푡) 푖 푅

where subscript i is used to indicate the i-th agent in the model, dSi, dIi and dRi respectively are change rates of the number of susceptible, infected, and recovered, in the i-th agent, Si, Ii, and Ri respectively are the number of susceptible, infected, and recovered animals before the current day for the i-th agent, S, I, and R respectively are the total number of susceptible, infected, and recovered animals before the current day for the

128 entire cluster, and dS and dR are calculated using the SIR model described above for the entire cluster.

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Appendix B: Supplementary figure

Figure B.1. Different number of runs for the first scenario in Kim et al. 2016. Each panel shows the variance at each time step. These results suggest that 100 runs are sufficient to capture reliable results.

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Appendix C: ODD protocol for the model in Chapter 5

This document describes modeling the effects of transhumance movement on the transmission of foot-and-mouth disease (FMD) following the Overview, Design concepts, and Details (ODD) protocol (V. Grimm et al., 2010; Volker Grimm et al.,

2006). We build the model in the MASON toolkit, which is a Java-based agent- simulation library (Luke et al., 2004).

OVERVIEW

Purpose. The purpose of the model is to examine the effects of the transhumance movements of mobile pastoralists in the Far North Region of Cameroon on the FMD transmission. This model addresses two main questions: 1) how do the movement patterns of mobile pastoralists impact on FMD transmission, and 2) what would have happened if there is a change in the regular transhumance movements?

Entities, state variables, and scales. The landscape of the model is 200 km by 200 km, which is simplified, based on the Far North Region of Cameroon. The landscape consists of 7 seasonal areas (four rainy and three dry season areas) and two different livestock density areas. Each seasonal area is a square, 30 km on a side, and is placed in a position that approximates relative geographic distance from one another (Figure 5.2). 131

Agents are divided into two types: sedentary agents and mobile agents. A sedentary agent represents a village, and a mobile agent represents a camp that consists of several mobile pastoralists. For this model, we used 5,000 sedentary agents and 500 mobile agents, and each sedentary and mobile agent consists of 100 and 500 animals, respectively.

Process overview and scheduling. The model proceeds in daily time steps and run for 5 years. Within each time step, mobile agents decide whether they stay at the current location or move toward the next location based on their mobility rules. If they decide to move, then they determine the next place according to their orbits. Once the locations of the mobile agents are settled, the model examines the spread of FMD virus. The model investigates all infected agents and the agents that are within a buffer of infected agents or have buffers that overlap the buffers of infected agents – neighboring agents. All neighboring agents to infected agents are set as an initial population in the epidemic model. After completion of the epidemic model, the updated values in each disease state 132 are redistributed back to each agent. This process continues until the end of the simulation. The model process is presented in the following pseudo code.

INITIALIZATION Set user defined parameters Create agent world and seasonal areas Create orbits for the mobile agents Place the mobile agents in the rainy seasonal areas Place the sedentary agents in the low and high livestock density areas

EACH TIME STEP Each mobile agent: If the time step is in the rainy or dry season If the agent stays at a location more than 55±35 days then Moves to a random location within the seasonal area End if Else If the agent stays at a location more than 4±2 days then Moves toward the next seasonal zone End if

All agents: Set up population groups For 1 to the total number of agents If an agent has at least one infected animal and has not been assigned to any population group then Assign this agent to a new population group Investigate the agents that neighbor this agent Assign the agents to the same population group with this agent End if Next agent

For 1 to the total number of population group Run the epidemic model Redistribute the updated values of each epidemic state to each agent Next population group Store the values of each epidemic state for each agent

DESIGN CONCEPTS

Emergence. Spatiotemporal dynamics of FMD epidemics throughout the region emerge from daily and seasonal movements of the mobile agents. 133

Sensing. Agents can sense nearby agents by checking whether or not their buffers are overlapped.

Interaction. By sharing the space, agents interact with each other and transmit the FMD virus. Because the distance between agents determines the interactions, they change depending on the movement of mobile agents at every time step.

Stochasticity. At the beginning of the simulation, sedentary agents are randomly distributed at a ratio of 2 to 8 in the low and high livestock density areas and mobile agents are randomly distributed in the rainy season areas according to their orbits. Within a seasonal area, the locations of mobile agents are chosen at random. The movement schedules of mobile agents also are based on the stochastic process. The movement schedules follow normal distributions of the mean arrival and leaving dates for each seasonal area. In addition, disease starts at the beginning of the simulation in a randomly selected sedentary agent within the shaded area in Figure 5.2.

Observation. The total number of individuals in each epidemic state (S, I and R) is collected at every time step.

DETAILS

Initialization. The model always starts on August 16 to be consistent with the survey data. FMD outbreak starts at day 1 and all agents are initially in the susceptible category.

Model parameters that are related to initialization are summarized in Table 5.2. The parameter values can be changed by the user.

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Input data. 10 orbits identified from the orbit analysis using transhumance survey data are read to assign the mobility rules to mobile agents and 7 seasonal areas and two high and low livestock density areas are imported.

Submodels. The model consists of two submodels.

Movement model: A mobile agent follows assigned orbit. When the mobile agent is in a season (i.e., between the arrival and leaving dates), the agent randomly chooses a location in the corresponding seasonal area, stays there for at least 20 days or up to three months, and continues to find a random location before the leaving date is reached. On the leaving date, the agent moves toward the next seasonal area in the orbit. In between the current and next seasonal areas, the agent makes a linear movement within the distance range between 9 to 11km that follows a uniform distribution and stays at the location for 2 to 6 days. The model assigns movement schedules that follow normal distributions of the mean arrival and leaving dates for each seasonal area to mobile agents. Thus, the agents who follow the same orbit have slightly different movement schedules.

Disease model: The epidemic follows a susceptible-infected-recovered (SIR) model with waning immunity. This model assumes that an infected individual moves from a susceptible to an infected state and infects other individuals. After a period of time, the individual finally recovers. Because we have run the model for multiple years, we assumed that immunity lasts for a limited period, and the recovered individuals move to the susceptible state (Laura W Pomeroy et al., 2015). We also considered births and deaths in a year. As a result, we used the following equations (Keeling & Rohani, 2008):

135 d푆 = 휇 + 휔푅 − 훽푆퐼 − 휇푆 d푡 d퐼 = 훽푆퐼 − 훾퐼 − 휇퐼 (1) d푡 d푅 = 훾퐼 − 휔푅 − 휇푅 d푡

where S is the number of susceptible individual animals in the population, I the number of infected animals, R the number recovered animals, μ the birth and death rate, ω the immunity rate, β the disease transmission rate, and γ the recovery rate. The disease transmission rate depends on the basic reproduction ratio, R0 = β/(γ +μ).

푆 푑푆 (푡) = 푖 푑푆(푡) 푖 푆 퐼 푑퐼 (푡) = 푖 푑퐼(푡) (2) 푖 퐼 푅 푑푅 (푡) = 푖 푑푅(푡) 푖 푅

136 where subscript i is used to indicate the i-th agent in the model; dSi, dIi, and dRi respectively are change rates of the number of susceptible, infected, and recovered, in the i-th agent; Si, Ii, and Ri respectively are the number of susceptible, infected, and recovered animals before the current day for the i-th agent; S, I, and R respectively are the total number of susceptible, infected, and recovered animals before the current day for the entire cluster; and dS and dR are calculated using the SIR model described above for the entire cluster.

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