As protection against infectious disease, immunity is conferred by one of two main defense mechanisms, namely (i) resistance generated by previous infection (known as natural immunity) or (ii) by being vaccinated (known as artificial immunity). To analyze, a modified SVIRS epidemic model is established that integrates the effects of the durability of protection and imperfectness in the framework of the human decision-making process as a vaccination game. It is supposed that immunized people become susceptible again when their immunity expires, which depends on the duration of immunity. The current theory for most voluntary vaccination games assumes that seasonal diseases such as influenza are controlled by a temporal vaccine, the immunity of which lasts for only one season. Also, a novel perspective is established involving an individual’s immune system combined with self-interest to take the vaccine and natural immunity obtained from infection by coupling a disease-spreading model with an evolutionary game approach over a long period. Numerical simulations show that the longer attenuation helps significantly to control the spread of disease. Also discovered is the entire mechanism of active and passive immunities, in the sense of how they coexist with natural and artificial immunity. Thus, the prospect of finding the optimal strategy for eradicating a disease could help in the design of effective vaccination campaigns and policies.

作为针对传染病的保护，免疫力是通过两种主要防御机制之一赋予的，即（i）先前感染产生的耐药性（称为自然免疫力）或（ii）接种疫苗（称为人工免疫力）。为了进行分析，建立了一个改进的SVIRS流行病模型，该模型将保护的持久性和不完善性的影响整合到了作为疫苗接种游戏的人类决策过程的框架中。据推测，免疫者的免疫力到期时，又会再次变得易感，这取决于免疫力的持续时间。当前大多数自愿疫苗接种游戏的理论都假设季节性疾病（例如流感）是由临时疫苗控制的，临时疫苗的免疫仅持续一个季节。也，建立了一个新颖的观点，将个人的免疫系统与自身利益相结合，从而通过长期将疾病传播模型与进化博弈方法相结合，来获取从感染中获得的疫苗和自然免疫。数值模拟表明，更长的衰减有助于显着控制疾病的传播。从主动免疫和被动免疫与自然免疫和人工免疫共存的意义上说，还发现了主动免疫和被动免疫的整个机制。因此，寻找根除疾病的最佳策略的前景可能有助于设计有效的疫苗接种运动和政策。数值模拟表明，更长的衰减有助于显着控制疾病的传播。从主动免疫和被动免疫与自然免疫和人工免疫共存的意义上说，还发现了主动免疫和被动免疫的整个机制。因此，寻找根除疾病的最佳策略的前景可能有助于设计有效的疫苗接种运动和政策。数值模拟表明，更长的衰减有助于显着控制疾病的传播。从主动免疫和被动免疫与自然免疫和人工免疫共存的意义上说，还发现了主动免疫和被动免疫的整个机制。因此，寻找根除疾病的最佳策略的前景可能有助于设计有效的疫苗接种运动和政策。