In the context of voluntary vaccination, we consider two additional provisions as well as pre-emptive vaccination for a unified model over epidemiology and evolutionary game theory to assess the extent to which advanced and late provisions restrict the spread of disease. To circumvent infection, people can be vaccinated pre-emptively before the epidemic season, but the imperfectness of vaccination or an unwillingness to be vaccinated may cause people instead to either be late-vaccinated or use self-protection. Here, self-protection corresponds to actions such as wearing a mask, washing hands, or using a mosquito net and is defined as the third strategy after pre-emptive vaccination (the first strategy) and late-vaccination (the second strategy). Our model can reproduce multiple social dilemma situations resulting from what is known as the vaccination dilemma (originating from preemptive vaccination), which works on a global time scale (i.e., repeated seasons approaching social equilibrium), and also from two other dilemmas due to late provisions, which work on a local time scale (i.e., every time step in a single season). To reproduce how an individual can acquire information for adaptation from neighbors or the society for a suitable provision, we introduce several strategy-updating rules for both global and local time scales and this behavioral feedback has a significant effect to reducing a transmissible disease. We also establish the social efficiency deficit (SED) indicator for a triple-dilemma game to quantify the existence of a social dilemma. Relying fully on a theoretical framework, our model provides a new perspective for evaluations: (i) how much more advantageous and effective pre-emptive vaccination is in eradicating a communicable disease compared with late provisions such as late vaccination and self-protection, and (ii) the extent of the social dilemma resulting from each of the three provisions, given the new idea of SED. The main effect of the triple-dilemma is that expensive provision displays no SED (no dilemma) until the efficiency or effectiveness of provisions reaches a certain level.

在自愿接种的情况下，我们考虑了两个额外的规定以及针对流行病学和进化博弈理论的统一模型的先行预防接种，以评估先进和晚期规定在多大程度上限制了疾病的传播。为了避免感染，可以在流行季节来临之前对人们进行预防接种，但是疫苗接种不完善或不愿进行疫苗接种可能会导致人们延迟接种疫苗或采取自我保护措施。在此，自我保护对应于诸如戴口罩，洗手或使用蚊帐之类的动作，并且被定义为先发制人疫苗接种（第一种策略）和后期疫苗接种（第二种策略）之后的第三种策略。我们的模型可以重现所谓的疫苗接种困境（源自先发制人的疫苗接种）所导致的多种社会困境，这种情况在全球时间范围内起作用（即，重复的季节接近社会平衡），也由于其他两个困境而导致在当地时间范围内（即单个季节中的每个时间步长）工作的规定。为了重现个人如何从邻居或社会获取适应性条款的信息，我们针对全球和本地时间尺度引入了一些策略更新规则，这种行为反馈对减少传染性疾病具有重要作用。我们还为三重困境游戏建立了社会效率赤字（SED）指标，以量化社会困境的存在。我们的模型完全依赖于理论框架，为评估提供了新的视角：（i）与后期提供的疫苗和自我保护等最新规定相比，在消灭传染病方面，有更多的优势和有效的先发性疫苗接种，以及（ ii）考虑到SED的新思想，这三项规定中的每一项所导致的社会困境的程度。三重困境的主要影响是，昂贵的准备金不会显示出SED（没有困境），直到准备金的效率或有效性达到一定水平为止。（ii）鉴于SED的新理念，这三项规定中的每一项所导致的社会困境的程度。三重困境的主要影响是，昂贵的准备金不会显示出SED（没有困境），直到准备金的效率或有效性达到一定水平为止。（ii）考虑到SED的新理念，这三项规定中的每一项所导致的社会困境的程度。三重困境的主要影响是，昂贵的准备金不会显示出SED（没有困境），直到准备金的效率或有效性达到一定水平为止。