Game Theory of Vaccination and Depopulation for Managing Avian
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bioRxiv preprint doi: https://doi.org/10.1101/348813; this version posted June 17, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 1 Game theory of vaccination and depopulation for managing avian 2 influenza on poultry farms 3 4 Alexis Delabouglise1, Maciej F Boni1 5 6 1Center for Infectious Disease Dynamics, Department of Biology, Pennsylvania State University, University Park, 7 USA 8 9 10 Keywords 11 Veterinary epidemiology, behavioral epidemiology, health economics, avian influenza, game 12 theory, epidemiological modelling 13 14 15 Word Count: 4269 16 17 18 Correspondence 19 Alexis Delabouglise 20 Millennium Sciences Complex 21 Department of Biology 22 Pennsylvania State University 23 University Park, PA, 16802 24 [email protected] 1 bioRxiv preprint doi: https://doi.org/10.1101/348813; this version posted June 17, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 25 Abstract 26 Highly pathogenic avian influenza is endemic in domestic poultry populations in East and South Asia and 27 is a major threat to human health, animal health, and the poultry production industry. The behavioral 28 response of farmers to the disease and its epidemiological effects are still poorly understood. We considered 29 a symmetric game in a region with widespread smallholder poultry production, where the players are broiler 30 poultry farmers and between-farm disease transmission is both environmental (local) and mediated by the 31 trade of infected birds. Three types of farmer behaviors were modelled: vaccination, depopulation, and 32 cessation of poultry farming. We found that the transmission level of avian influenza through trade 33 networks had strong qualitative effects on the system’s epidemiological-economic equilibria. In the case of 34 low trade-based transmission, when the monetary cost of infection is sufficiently high, depopulation 35 behavior persists and maintains a disease-free equilibrium. In the case of high trade-based transmission, 36 depopulation behavior has perverse epidemiological effects – as it accelerates the spread of disease via 37 poultry traders – but has a high enough payoff to farmers that it persists at the system’s game-theoretic 38 equilibrium. In this situation, state interventions should focus on making effective vaccination technologies 39 available at a low price rather than penalizing infected farms. Our results emphasize the need in endemic 40 countries to further investigate the commercial circuits through which birds from infected farms are traded. 2 bioRxiv preprint doi: https://doi.org/10.1101/348813; this version posted June 17, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 41 Introduction 42 Behavioral epidemiology – the study of human behavioral responses to infectious disease circulation – has 43 been receiving an increasing amount of research attention over the last two decades (1). The behavioral 44 responses of humans to disease can generate unexpected externalities resulting in both positive and negative 45 feedback in the infection process, justifying the application of game theory to questions in the decentralized 46 control of infectious disease. Examples of theoretical advances in this field have focused on the adoption 47 of voluntary vaccination programs (2), the effects of endogenous vs government-recommended social 48 distancing strategies (3), and the willingness of states to disclose information on disease outbreaks (4). A 49 recent empirical study, based on time series of reports of social contacts, confirmed that voluntary social 50 distancing behavior affected the dynamics of H1N1 influenza epidemics in the US (5). 51 Although the effects of human behavior on the epidemiology of livestock disease are well- 52 documented, empirical studies on the effects of disease on human behavior are rare (6, 7). In livestock 53 disease epidemiology, it is reasonable to assume that producers primarily aim to maximize their protein 54 production or revenue and minimize their farm expenses; this principle may be used to predict livestock 55 owners’ behavioral response to disease risk. From a social planner’s perspective an additional optimization 56 is centered on the choice of public intervention, balancing the social need for affordable poultry products, 57 the welfare of actors in livestock value chains, and protecting public health. Therefore, any particular 58 surveillance and control policy must be evaluated by comparing its associated gains in public health with 59 its effect on producers’ income and consumers’ access to livestock products. 60 Highly pathogenic avian influenza (HPAI) is a zoonotic livestock disease motivating substantial 61 state intervention. HPAI outbreaks have occurred regularly in eastern and southern Asia, Egypt, and West 62 Africa since 2003 (8-10). HPAI has also been reported in Europe and North America (9). Some avian 63 influenza virus strains of the H5, H7, and H9 subtypes have the ability to cause severe and fatal disease in 64 humans. Therefore, poultry originating from farms contaminated with HPAI are potentially harmful to 65 farmers, consumers, and other persons handling poultry. While human infections with these subtypes are 66 rare, their case fatality rates are generally higher than 25% (11). In addition, the risk that such viruses 67 acquire a phenotype of human-to-human transmission constitutes a major global health threat and justifies 68 national-level interventions to reduce the exposure of humans to infected poultry (12). Since the emergence 69 and global spread of the H5N1 subtype of HPAI in 2003, interventions have mainly focused on 70 strengthening avian disease surveillance, preventive culling of domestic birds in outbreak areas, and 71 restrictions on poultry trade; in addition, Vietnam and China implemented mandatory poultry vaccination 72 programs (13, 14). A socio-economic field study conducted in Vietnam showed that farmers fear HPAI 3 bioRxiv preprint doi: https://doi.org/10.1101/348813; this version posted June 17, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 73 detection by the surveillance system not so much because of the risk of mandatory culling but because of 74 its adverse effect on the sale price of poultry (15). 75 In a theoretical model investigating individual responses of poultry farmers to price fluctuations, 76 the main finding for density-dependent transmission was that preventive culling of and compensation for 77 poultry can have perverse effects as it may incentivize an increase in farm size (higher average poultry price 78 incentivizes more production), while investments in surveillance, diagnostics, and targeted penalties were 79 found to lower overall health risk (for both frequency- and density-dependent transmission) (16). These 80 findings are in agreement with general economic models describing moral hazards and adverse selection 81 issues associated with the indemnification of farms affected by diseases (17-19). According to another 82 economic model applied to HPAI, compensation accompanying preventive culling policies should be 83 indexed to the prevention effort invested by farmers (20). These studies focus on the individual responses 84 of farmers and, as such, do not account for population-level externalities (e.g. between-farm infection risk 85 or market price). According to a generic game theory model focusing on prevention practices, enforcing 86 penalties on infected farms seems to be an appropriate way of incentivizing disease control in the private 87 sector, while policies based on indemnification may discourage prevention efforts (19). 88 The present study aims at modeling the behavioral responses of a heterogeneous group of poultry 89 farmers under different economic and epidemiological conditions. We introduce a symmetric population 90 game for this purpose, with broiler poultry farmers as players, and we link this to a compartmental model 91 of between-flock disease transmission. 92 93 Model 94 1. Description of the system 95 Our system consists of a population of broiler poultry farmers who purchase, grow, and sell flocks of 96 domestic broiler poultry for the purpose of income. Farmers purchase day-old chicks and sell them as 97 finished birds after a given growing period. Flocks of broiler poultry are kept in coops, and coops may be 98 empty if the opportunity cost of poultry farming is too high. Poultry flocks occupying coops are initially 99 disease-free and can be infected in the course of the growing period if the virus is introduced in the flock. 100 The propagation of the disease in each coop is not modeled; flocks are simply assumed to be infected or 101 uninfected. Coops lose their infected status at the time of depopulation, when infected poultry flocks are 102 sold to traders and replaced by susceptible flocks. Poultry flocks are always sold but the revenue generated 103 by a flock depends on both its growing period (which determines poultry weight) and its infection status 104 (Supplementary Information 1A). In a disease-free environment, farmers apply a constant optimal −1 105 growing period 휎∅ , and 휎∅ is the rate of poultry removal (sale) from farms (Supplementary Information 4 bioRxiv preprint doi: https://doi.org/10.1101/348813; this version posted June 17, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.