Dynamic Transmission Models: the Impact of Behavioural Feedbacks And
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Dynamic Transmission Models: The Impact of Behavioural Feedbacks and Parametrization Methods on Disease Intervention Effectiveness by Michael Andrews A Thesis presented to The University of Guelph In partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics Guelph, Ontario, Canada c Michael Andrews, October, 2016 ABSTRACT DYNAMIC TRANSMISSION MODELS: THE IMPACT OF BEHAVIOURAL FEEDBACKS AND PARAMETRIZATION METHODS ON DISEASE INTERVENTION EFFECTIVENESS Michael Andrews Advisor: University of Guelph, 2016 Chris T. Bauch Infectious diseases impose significant health and economic burdens across the world, continuously threatening human quality of life. Mathematical models of infectious dis- ease epidemiology can help to gain insight on potential health outcomes of a population that is vulnerable to disease spread. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccina- tion choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. In this thesis, we present three models of disease spread using the dynamic transmis- sion and behaviour-disease modelling frameworks. Firstly, we investigate an age-stratified compartmental model of influenza transmission and the impact of estimating this model’s parameters using different surveillance data has on population level outcomes. In the latter two models, we remove random mixing assumptions and incorporate an individual-based approach. We also simultaneously integrate an individual’s decision making processes for utilizing two fundamental disease interventions: vaccination and NPIs. In the past, mod- els have only considered the use of these interventions separately. All of our approaches focus on examining health outcomes of populations that are exposed to acute self-limited diseases, and offering insight on the effectiveness of disease mitigation strategies. iv To my parents, who have always been supportive of my academic endeavours. v Table of Contents List of Tables viii List of Figures x 1 Introduction 1 1.1 Infectious Disease Burdens . .1 1.2 Infectious Disease Modelling . .3 1.2.1 Homogeneous Models . .4 1.2.2 Network Models and Heterogeneous Contact Patterns . .6 1.2.3 Deterministic and Stochastic Modelling . .9 1.3 Disease Interventions . 10 1.3.1 Vaccination . 11 1.3.2 Non-Pharmaceutical Interventions . 12 1.4 Behavioural Epidemiology of Infectious Diseases . 13 1.4.1 Example of a Behaviour-Disease System . 16 1.5 Overview and Objectives . 19 2 Parameter Estimation in a Dynamic Model of Influenza Transmission Using Laboratory Confirmed Influenza Cases 21 2.1 Chapter Abstract . 21 2.2 Introduction . 22 2.3 Methods . 24 2.3.1 Population Demographics . 25 2.3.2 Influenza Incidence Data and Epidemiology . 25 2.3.3 Vaccination . 27 2.3.4 Model Structure . 28 2.3.5 Parameter Fitting . 30 Longitudinal Method . 31 Cross-Sectional Method . 33 2.4 Results . 35 vi 2.4.1 Parameter Fitting Comparison . 35 2.4.2 Projected Impact of Expanded Vaccination Coverage . 38 2.5 Discussion . 41 3 The Impacts of Simultaneous Disease Intervention Decisions on Epidemic Out- comes 45 3.1 Chapter Abstract . 45 3.2 Introduction . 47 3.3 Methods . 52 3.3.1 Disease Dynamics . 52 3.3.2 Contact Network . 53 3.3.3 Non-Pharmaceutical Interventions and Vaccination . 53 3.4 Results . 57 3.4.1 Baseline Dynamics . 57 3.4.2 Transmission Rate . 61 3.4.3 Vaccine Efficacy . 65 3.4.4 Pairwise Correlations . 67 3.5 Discussion . 70 3.6 Supporting Information . 75 3.6.1 Asymptomatic Cases . 75 3.6.2 Network Types . 78 3.6.3 Pairwise Analysis . 84 4 Disease Interventions Can Interfere With One Another Through Disease- Be- haviour Interactions 86 4.1 Chapter Abstract . 86 4.2 Introduction . 88 4.3 Model . 91 4.3.1 Vaccination . 91 4.3.2 Non-Pharmaceutical Interventions . 97 4.3.3 Transmission Dynamics . 99 4.3.4 Model Calibration . 101 4.4 Results . 103 4.4.1 Baseline Scenario . 103 4.4.2 Interventions Can Interfere With One Another . 104 4.4.3 Determining Which Interventions Interfere Most Strongly . 109 Impact of Interference on Intervention Uptake Rates . 109 Impact of Interference on Influenza Incidence . 110 4.4.4 Understanding What Drives Different Levels of Interference for Different Interventions . 114 4.5 Discussion . 117 vii 5 Conclusion 122 5.1 Conclusions and Future Work . 122 References 125 viii List of Tables 2.1 Parameter Descriptions . 34 2.2 Best fitting parameter values (mean and standard deviation) for the longi- tudinal method. 36 2.3 Best fitting parameter values (mean and standard deviation) for the cross- sectional method. 37 2.4 Mean number of cases for influenza strains A and B under different vacci- nation scenarios. 40 3.1 Baseline Parameter Values. 57 3.2 Epidemic final sizes (symptomatic cases only) with delayed vaccine avail- ability. β = 0.004 ............................... 76 3.3 Epidemic final sizes (symptomatic cases only) with delayed vaccine avail- ability. β = 0.005 ............................... 76 3.4 Epidemic final sizes (symptomatic cases only) with delayed vaccine avail- ability. β = 0.006 ............................... 77 3.5 Epidemic final sizes corresponding to vaccine efficacy (symptomatic cases only). 77 3.6 Population vaccine uptake corresponding to vaccine efficacy. 77 3.7 Epidemic final sizes with delayed vaccine availability (random network). β = 0.00485 .................................. 79 3.8 Epidemic final sizes with delayed vaccine availability (random network). β = 0.00585 .................................. 80 3.9 Epidemic final sizes with delayed vaccine availability (random network). β = 0.00685 .................................. 80 3.10 Epidemic final sizes corresponding to vaccine efficacy (random network). 81 3.11 Population vaccine uptake corresponding to vaccine efficacy (random net- work). 81 3.12 Epidemic final sizes with delayed vaccine availability (power law network). β = 0.055 ................................... 82 ix 3.13 Epidemic final sizes with delayed vaccine availability (power law network). β = 0.075 ................................... 83 3.14 Epidemic final sizes with delayed vaccine availability (power law network). β = 0.095 ................................... 83 3.15 Epidemic final sizes corresponding to vaccine efficacy (power law network). 83 3.16 Population vaccine uptake corresponding to vaccine efficacy (power law network). 84 4.1 Model parameters with baseline values and sources. 96 4.2 Sampling ranges for parameters used to obtain 100 baseline sets. 103 4.3 Acceptance ranges for simulation averages across 30 seasons. 103 x List of Figures 1.1 Time series of an epidemic. 18 2.1 Diagram of the age-stratified SIRS compartmental model with vaccination. 31 2.2 Time series of confirmed influenza cases. 35 2.3 Age-stratified cumulative cases for influenza compared to empirical targets. 38 2.4 Time series of confirmed influenza A and B cases in our model with differ- ent vaccination scenarios. 40 2.5 Age stratified cumulative cases in our model for influenza A and B with different vaccination scenarios. 42 3.1 Time series of an epidemic, 95% confidence intervals shown every 10 days around the mean of 500 realizations. 60 3.2 Time series of infection prevalence with the vaccine-only scenario, the NPI-only scenario, and the combined scenario. 62 3.3 Epidemic final sizes with respect to when vaccination is made available. 64 3.4 Epidemic measures with respect to transmission rate. 66 3.5 Effects of vaccine efficacy between scenarios with and without NPIs. 68 3.6 Time series of epidemics over different values of σ, the weighting for global versus local information. 71 3.7 Frequency of node degrees in the empirically based network. 78 3.8 Pairwise sensitivity analysis of parameters λ and γ.............. 85 4.1 Vaccination and NPI decisions. 92 4.2 Seasonal time series. 94 4.3 Impact of vaccine introduction. 105 4.4 The effects of social parameters on interventions. 107 4.5 The effects of infection and vaccination costs on interventions. 108 4.6 Interference between vaccination and NPIs. 112 4.7 Interference between vaccination and NPIs. 113 4.8 The effects of NPI efficacy. 115 xi 4.9 The effects of vaccine efficacy. 116 1 Chapter 1 Introduction 1.1 Infectious Disease Burdens Infectious diseases impose significant health and economic burdens across the world, continuously threatening human quality of life (Klein et al., 2007). Throughout history, infectious disease epidemics have negatively impacted human societies causing significant morbidity and mortality. For example, the “Black Death” in the mid 1300’s caused millions of deaths, eliminating a considerable portion of the human population at the time (Kelly, 2006). Also, the cholera epidemic in the 19th century in Europe, and eventually spreading to North America, killed hundreds of thousands. In fact, this disease still affects developing countries today (Barua, 1992). Cholera in particular is an important historical disease, as a physician named John Snow made major groundbreaking contributions to the field of epidemiology through his studies of cholera throughout his medical career (Timmreck, 2 2002). More recently, the 20th century was also marred by disease outbreaks. Beginning in 1918, an influenza pandemic swept across the world, killing millions (Crosby, 1989). This particular flu was unordinary in that many of the deaths occurred amongst young adults- an unusual characteristic of influenza (Taubenberger et al., 2000). Two more influenza pandemics also occurred in 1957 (the Asian flu) and 1968 (the Hong Kong flu). These viruses also spread worldwide, with infants and the elderly being the most likely to suffer severe complications (Hsieh et al., 2006). Finally, in the late 1970’s and early 1980’s, patients with symptoms such as fever, weight loss, and swollen lymph nodes began to appear in California and New York. These cases would soon be identified as HIV/AIDS, and the HIV virus has since been a worldwide pandemic responsible for the deaths of millions (Grmek, 1990). The 21st century has been affected by several disease epidemics as well. In 2003, an outbreak of severe acute respiratory syndrome (SARS) was reported in China, prompting health agencies to issue global alerts.