Imperfect vaccine can yield multiple Nash equilibria in vaccination games
Imperfect vaccine can yield multiple Nash equilibria in vaccination games
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DOI：
10.1016/j.mbs.2023.108967
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发表时间：
2023-01-20
影响因子：
4.3
通讯作者：
Taylor, Dewey
中科院分区：
文献类型：
--
作者：
Augsburger, Ian B.;Galanthay, Grace K.;Taylor, Dewey
随着传染病继续威胁着地球仪各地的社区，人们面临着接种或不接种疫苗的选择。许多因素影响这一决定，如疾病的成本，感染疾病的机会，人口疫苗接种覆盖率和疫苗的有效性。近年来，虽然个人根据自己的兴趣决定是否接种疫苗的疫苗接种游戏越来越受欢迎，但疫苗的不完美性迄今为止一直是一个被忽视的方面。在本文中，我们研究了一个不完美的疫苗接种游戏的结果的影响。我们使用一个简单的SIR房室模型的基础模型的疾病传播。我们通过在出生时接种疫苗来模拟疫苗的不完善性，并保持接种疫苗的个体被感染的可能性。我们得到明确的条件存在不同的纳什均衡，接种疫苗的游戏的解决方案。博弈的结果取决于疾病传播动力学（基本繁殖数）、感染的相对成本和疫苗效力之间复杂的相互作用。我们发现，对于基本繁殖数相对较低（小于约2.62）的疾病，完美或不完美疫苗的结果之间存在一点差异，因此假设完美疫苗足够好的简单模型。然而，当基本繁殖数大于2.62时，与完美疫苗的情况不同，可能存在多重均衡。此外，除非有一个强制性的疫苗接种政策，将推动疫苗接种覆盖率高于不稳定的纳什均衡值，人口最终可能会滑向“不接种“状态。因此，对于基本繁殖数相对较高的疾病，模型中应明确考虑疫苗不完美的可能性。
As infectious diseases continue to threaten communities across the globe, people are faced with a choice to vaccinate, or not. Many factors influence this decision, such as the cost of the disease, the chance of contracting the disease, the population vaccination coverage, and the efficacy of the vaccine. While the vaccination games in which individuals decide whether to vaccinate or not based on their own interests are gaining in popularity in recent years, the vaccine imperfection has been an overlooked aspect so far. In this paper we investigate the effects of an imperfect vaccine on the outcomes of a vaccination game. We use a simple SIR compartmental model for the underlying model of disease transmission. We model the vaccine imperfection by adding vaccination at birth and maintain a possibility for the vaccinated individual to become infected. We derive explicit conditions for the existence of different Nash equilibria, the solutions of the vaccination game. The outcomes of the game depend on the complex interplay between disease transmission dynamics (the basic reproduction number), the relative cost of the infection, and the vaccine efficacy. We show that for diseases with relatively low basic reproduction numbers (smaller than about 2.62), there is a little difference between outcomes for perfect or imperfect vaccines and thus the simpler models assuming perfect vaccines are good enough. However, when the basic reproduction number is above 2.62, then, unlike in the case of a perfect vaccine, there can be multiple equilibria. Moreover, unless there is a mandatory vaccination policy in place that would push the vaccination coverage above the value of unstable Nash equilibrium, the population could eventually slip to the "do not vaccinate"state. Thus, for diseases that have relatively high basic reproduction numbers, the potential for the vaccine not being perfect should be explicitly considered in the models.