Jnawali Kamal, Morsky Bryce, Poore Keith, Bauch Chris T
Department of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph, Ontario, N1G 2W1, Canada.
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada.
Infect Dis Model. 2016 Sep 2;1(1):40-51. doi: 10.1016/j.idm.2016.07.003. eCollection 2016 Oct.
The potential for emergence of antiviral drug resistance during influenza pandemics has raised great concern for public health. Widespread use of antiviral drugs is a significant factor in producing resistant strains. Recent studies show that some influenza viruses may gain antiviral drug resistance without a fitness penalty. This creates the possibility of strategic interaction between populations considering antiviral drug use strategies.
To explain why, we develop and analyze a classical 2-player game theoretical model where each player chooses from a range of possible rates of antiviral drug use, and payoffs are derived as a function of final size of epidemic with the regular and mutant strain. Final sizes are derived from a stochastic compartmental epidemic model that captures transmission within each population and between populations, and the stochastic emergence of antiviral drug resistance. High treatment levels not only increase the spread of the resistant strain in the subject population but also affect the other population by increasing the density of the resistant strain infectious individuals due to travel between populations.
We found two Nash equilibria where both populations treat at a high rate, or both treat at a low rate. Hence the game theoretical analysis predicts that populations will not choose different treatment strategies than other populations, under these assumptions. The populations may choose to cooperate by maintaining a low treatment rate that does not increase the incidence of mutant strain infections or cause case importations to the other population. Alternatively, if one population is treating at a high rate, this will generate a large number of mutant infections that spread to the other population, in turn incentivizing that population to also treat at a high rate. The prediction of two separate Nash equilibria is robust to the mutation rate and the effectiveness of the drug in preventing transmission, but it is sensitive to the volume of travel between the two populations.
Model-based evaluations of antiviral influenza drug use during a pandemic usually consider populations in isolation from one another, but our results show that strategic interactions could strongly influence a population's choice of antiviral drug use policy. Furthermore, the high treatment rate Nash equilibrium has the potential to become socially suboptimal (i.e. non-Pareto optimal) under model assumptions that might apply under other conditions. Because of the need for players to coordinate their actions, we conclude that communication and coordination between jurisdictions during influenza pandemics is a priority, especially for influenza strains that do not evolve a fitness penalty under antiviral drug resistance.
流感大流行期间抗病毒药物耐药性的出现可能性引发了对公共卫生的高度关注。抗病毒药物的广泛使用是产生耐药菌株的一个重要因素。最近的研究表明，一些流感病毒可能在不影响适应性的情况下获得抗病毒药物耐药性。这就产生了考虑抗病毒药物使用策略的人群之间进行策略互动的可能性。
为了解释原因，我们开发并分析了一个经典的两人博弈理论模型，其中每个参与者从一系列可能的抗病毒药物使用速率中进行选择，收益是根据常规菌株和突变菌株的疫情最终规模的函数得出的。最终规模来自一个随机 compartmental 疫情模型，该模型捕捉了每个群体内部以及群体之间的传播，以及抗病毒药物耐药性的随机出现。高治疗水平不仅会增加耐药菌株在目标人群中的传播，还会因人群之间的流动而增加耐药菌株感染个体的密度，从而影响其他人群。
我们发现了两个纳什均衡，即两个群体都以高比率进行治疗，或者都以低比率进行治疗。因此，在这些假设下，博弈理论分析预测人群不会选择与其他人群不同的治疗策略。人群可能会选择通过维持低治疗率来进行合作，这样既不会增加突变菌株感染的发生率，也不会导致病例输入到其他人群中。或者，如果一个群体以高比率进行治疗，这将产生大量传播到其他人群的突变感染，进而促使该人群也以高比率进行治疗。两个独立纳什均衡的预测对于突变率和药物预防传播的有效性具有稳健性，但对两个群体之间的流动量敏感。
大流行期间基于模型对抗病毒流感药物使用的评估通常将人群彼此孤立地考虑，但我们的结果表明，策略互动可能会强烈影响人群对抗病毒药物使用政策的选择。此外，在可能适用于其他条件的模型假设下，高治疗率纳什均衡有可能变得在社会上次优（即非帕累托最优）。由于参与者需要协调他们的行动，我们得出结论，流感大流行期间各辖区之间的沟通与协调是当务之急，特别是对于在抗病毒药物耐药性下不会进化出适应性代价的流感毒株。
