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Introduction Model Development A Spatial Agent-Based Model of Anopheles vagus for Malaria Epidemiology Md. Zahangir Alam1, S. M. Niaz Arifin2, H. M. Al-Amin3, Mohammad Shafiul Alam3, M. Sohel Rahman1 1Department of Computer Science & Engineering (CSE), Bangladesh University of Engineering & Technology (BUET), Dhaka 1000, Bangladesh 2Department of Computer Science and Engineering, University of Notre Dame, IN 46556, USA 3International Centre for Diarrhoeal Disease Research Bangladesh (icddr,b), Dhaka, Bangladesh Introduction Malaria is the ninth largest cause of global human mortality and morbidity [1, 2]. About 3.3 billion people in 99 countries are reported to be at risk of malaria [3]. Each year, it kills around two million people [4], most of which are young children in sub-Saharan Africa [5]. Being a mosquito-borne disease, malaria is transmitted among humans by female mosquitoes of the genus Anopheles [6]. Among the approximately 430 Anopheles species, only 30-40 are known to transmit malaria in nature [6]. Anopheles gambiae is responsible for transmitting the most dangerous malaria parasite, namely, Plasmodium falciparum, among humans. On the other hand, Anopheles vagus is another species that transmits Plasmodium vivax, another dangerous parasite causing 47% malaria cases in the Asia-Pacific Region [7, 8]. An. vagus is widely distributed in Asia, particularly in Bangladesh, Cambodia, China (including Hong Kong), India, Indonesia, Laos, Malaysia, Mariana Islands, Myanmar, Nepal, Philippines, Sri Lanka, Thailand, and Vietnam [10-12]. In the recent past, several mathematical (equation-based) and agent-based models (ABMs) of for malaria have been developed to model the life cycle of An. gambiae [13-19, 22, 23]. The spatial dimension, using a landscape-based approach, is also described in detail by some of the models [14, 15]. However, despite its wide distribution in the Asia-Pacific Region, no model of An. vagus has yet been developed or reported in the literature. In this paper, we describe the design, implementation, and some preliminary results from of an ABM of for An. vagus. The ABM, denoted as ABMvagus, is developed by modifying an established existing ABM of for An. gambiae (referred to as ABMgambiae henceforth) from the University of Notre Dame [13-16]. We describe the life cycle modeling of An. vagus, based on its important biological parameters, and report the effect of temperature on the abundance of An. vagus. Obtaining monthly An. vagus female abundance data from field studies [10], we validate the model’s output against the real data. Model Development Like ABMgambiae, ABMvagus includes two distinct phases in the An. vagus life cycle, namely, aquatic and adult. The aquatic phase consists of three stages, namely, egg, larva and pupa. The adult phase consists of five stages, namely, immature adult, mate seeking, blood meal seeking, blood meal digesting, and gravid. The major differences between the two ABMs are reported in Table 1. Both An. vagus and An. gambiae pass through the same stages during their life cycle [6]. However, An. vagus mostly rests indoors [20]. ABMvagus primarily considers the eight stages, and modifies/extends ABMgambiae according to recent field data for each stage. Table 1: Differences between the ABMs of Anopheles vagus and Anopheles gambiae. DMR denotes the daily mortality rate. Model Feature An. vagus An. gambiae Reference Reference Egg 60% eggs are developed [25,26] Development [13] development within 2 days and remaining (incubation and and DMR 40% within 3 days in normal hatching) is temperature. DMR is 10%. temperature dependent, equation-based. DMR is 10%. Larval Four sub-stages: 1st instar, 2nd [25,26] Development is [13] development instar, 3rd instar & 4th instar temperature dependent. and DMR with different duration. DMRs in each sub-stage are 15%, 10%, 10%, and 10%, respectively. Pupa 40% pupae are developed [25,26] Development is [13] development within the first 24 hours and temperature dependent, and DMR 60% within the next 30 hours. equation-based. DMR is 5%. DMR is 10% Immature Adult 10% emergence on the 6th day, [25,26] Development is [13] 10% on the 7th day, 40% on temperature dependent, the 8th day, 30% on the 9th equation-based. day, and 10% on the 10th day. DMR is 10% Blood Meal Continues until it gets blood 24 Continues until it gets [13] Seeking meal or dies. The most blood meal or dies. The effective time-window for effective time-window host-seeking is 5.00am to for host-seeking is 6.00am. 6.00pm to 6.00am. Host-seeking occurs as follows: at 8:30 pm: 0%, 9:30 pm: 13.67%, 10:30 pm: 15.83%, 11:30 pm: 10.8%, 12:30 am: 7.2%, 1:30 am: 0.72%, 2:30 am: 0%, 3:30 am: 0.72%, 4:30 am: 1.44%, 5:30 am: 35.25%, 6:30 am: 14.39%, 7:30 am: 0%. In the model, mosquitoes and aquatic habitats are modeled as agents. A mosquito agent stays in each stage for certain duration, with probabilistic transitions to the next stage. For example, an agent oviposits 60% of the eggs on the 2nd day, and the remaining 40% eggs on the 3rd day in normal temperature (i.e, 26- 30°C). For each stage, the daily mortality rate (DMR), obtained from field data, is applied after it is converted to hourly mortality rates (for each simulated hourly timestep) to match ABMgambiae. P. vivax malaria transmission depends on several factors, including vector availability, biting rates, etc. Many of these factors are also influenced by weather and climate variables, especially temperature [11]. For a particular geographic region, daily temperature primarily affects larval development and blood meal digesting durations. Hence, ABMvagus includes a temperature profile module, in which annual temperature data is loaded, and the simulations are fed with daily temperature data derived from the profile. Field Data Collection Field data on An. vagus abundance are collected from a study in the hill tract district of Bandarban, Bangladesh, which reports abundances of several local species as follows: An. jeyporiensis: 18.9%, An. vagus: 16.8%, and An. kochi: 14.4% [10]. Monthly An. vagus female abundance is reported to reach the highest level during March, followed by an immediate sharp decrease during April. Daily temperature data is also collected from the Soil Resource Development Institute for Bandarban, Bangladesh [21]. Verification & Validation The conceptual model is verified through early testing to check whether the implementation is a correct realization of the concepts adopted from the field data. Two early implementations are compared with each other: one with twelve stages in which the Larva stage is further sub-divided into four sub-stages (see Table 1), and the other with eight stages where larval development is calculated with a temperature- dependent equation. Results from both implementations are compared in order to select the more correct one (in terms of realization of the conceptual model). The model is also validated against field data (as described above) [10, 21]. Results Some preliminary results derived from ABMvagus are shown in Figures 1 and 2. Figure 1. Female Abundance in 4 years simulation run: Female Abundance (FA) from a 4-years simulation run. The annual pattern of An. vagus abundance is directly regulated by temperature. The x- axis denotes simulation time (in days) and the y-axis denotes mosquito abundance. Figure 2: Model Validation. An. vagus abundances from the simulations of three consecutive years are compared to field data, showing that the simulated results are very close to field data. This helps to ensure the validity of the ABM. References 1. Welcome Trust, Malaria Atlas Project (2010). Available from http://www.map.ox.ac.uk 2. WHO, Global burden of disease (2008). http://www.who.int/healthinfo/global_burden_disease/en/ 3. WHO, Larval source management – a supplementary measure for malaria vector control. An operational manual (July 2013). http://www.who.int/malaria/publications/atoz/9789241505604/en/ 4. CDC (Centers for Disease Control and Prevention), Malaria Facts. http://www.cdc.gov/malaria/facts.htm 5. Snow R.W., Guerra C.A., Noor A.M., Myint H.Y., Hay S.I.: “The global distribution of clinical episodes of Plasmodium falciparum malaria.”, Nature, 343 (7030): 214-7, 2005 6. CDC (Centers for Disease Control and Prevention), Anopheles Mosquitoes. http://www.cdc.gov/malaria/biology/mosquito 7. Maheshwary N.P., Majumdar S., Chowdhury A.R.,Fruque M.S., Montanari R.M.: “Incrmination of Anopheles vagus Donitz, 1902 as an Epidemic Malaria Vector in Bangladesh. Indian Journal of Malariology”, Vol. 31, March 1994, pp. 35-38. 8. Lynch C., Hewitt S.: “Malaria in the Asia-Pacific: Burden, success and challenges”, October 2012. 9. Gu W. and Novak R. J.: “Agent-based modelling of mosquito foraging behavior for malaria control”, Transactions of the Royal Society of Tropical Medicine and Hygiene, 103(11):1105- 1112, 2009. 10. Alam M.S., Chakma S., Khan W.A., Glass G.E., Mohon A.N., Elahi R., Norris L.C., Podder M.P., Ahmed S., Haque R., Sack D.A., Sullivan D.J., Norris D.E.: “Diversity of anopheline species and their Plasmodium infection status in rural Bandarban, Bangladesh”, Parasites & Vectors 2012, 5:150 11. Wardrop N.A, Barnett A.G., Atkinson J. and Clements A.C.: “Plasmodium vivax malaria incidence over time and its association with temperature and rainfall in four counties of Yunnan Province, China”, Malaria Journal 2013, 12:452 12. Rueda, L.M., Pecor, J.E. and Harrison, B.A.: “Updated distribution records for Anopheles vagus (Diptera: Culicidae) in the Republic of Philippines, and considerations regarding its secondary vector roles in Southeast Asia”, Tropical Biomedicine 28(1): 181–187 (2011) 13. Zhou Y., Arifin S.M.N., Genetile J., Kurtz S.J., Davis G.J., Wendelberger B.A, Madey G.: “An Agent-based Model of the Anopheles gambiae Mosquito Life Cycle”, SCSC '10 Proceedings of the 2010 Summer Computer Simulation Conference, Pages 201-208, 2010-07-11 (yyyy-mm-dd) 14.
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