进化的疫苗接种游戏与过早的疫苗，以打击正在进行的致命的大流行病
Evolutionary Vaccination Games with premature vaccines to combat ongoing deadly pandemic
摘要：
我们考虑一个疫苗接种游戏，其结果是引入了不成熟的和可能稀缺的疫苗，以对抗致命的流行病。不确定主体在诸多不确定性中的反应，使得这一博弈与以往的研究完全不同。我们构建了一个框架，结合SIS流行病模型与各种动态行为的疫苗接种反应和人口统计方面。每种药剂的反应受到疫苗接种犹豫和紧迫性的影响，这是由于他们对疫苗的功效和副作用、疾病特征和相关报告信息（例如，副作用、疾病统计等）。基于这些方面，我们确定了对静态突变稳定的反应。通过分析所得到的常微分方程的吸引子，我们观察到有趣的图案在进化稳定（ES）策略下的系统的极限状态，作为各种定义参数的函数。有完全根除疾病的反应（在限制状态），但没有一种对突变是稳定的。此外，无论疾病死亡率如何，疫苗接种丰度导致ES限制状态下的感染分数较高。
英文摘要：
We consider a vaccination game that results with the introduction of premature and possibly scarce vaccines introduced in a desperate bid to combat the otherwise ravaging deadly pandemic. The response of unsure agents amid many uncertainties makes this game completely different from the previous studies. We construct a framework that combines SIS epidemic model with a variety of dynamic behavioral vaccination responses and demographic aspects. The response of each agent is influenced by the vaccination hesitancy and urgency, which arise due to their personal belief about efficacy and side-effects of the vaccine, disease characteristics, and relevant reported information (e.g., side-effects, disease statistics etc.). Based on such aspects, we identify the responses that are stable against static mutations. By analysing the attractors of the resulting ODEs, we observe interesting patterns in the limiting state of the system under evolutionary stable (ES) strategies, as a function of various defining parameters. There are responses for which the disease is eradicated completely (at limiting state), but none are stable against mutations. Also, vaccination abundance results in higher infected fractions at ES limiting state, irrespective of the disease death rate.
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