We explore the complex dynamics of epidemics, considering the significant effects of disease transmission, newborn individuals, and mortality rate. Employing an evolutionary game theory approach, we model the vaccination aspect for newborns, incorporating potential periodic behavior. The goal is to create an engaging simulation that underscores the criticality of timely infant vaccinations. By introducing periodic elements, the game adds complexity, fostering player participation and awareness of vaccination schedules. In contrast to traditional intervention game models focused on adult vaccine behavior, our approach recognizes the unique challenges posed by newborn vaccination. We address the limitations of existing models by developing a generalized compartmental model, accommodating infection duration distribution, and accurately capturing both periodic and non-periodic disease trajectories. The results show that higher efficacy in a newborn vaccine program can potentially eradicate the disease, but higher effectiveness and cost may deter vaccination. Increased motivation cost boosts vaccination rates without impacting epidemic size, whereas lower costs stabilize vaccination rates. Lower vaccine costs call for increased government investment to counter hesitancy. However, reduced efficacy and lower motivation lead to higher Vaccine Fear Scores, discouraging participation. Our work also offers a unique perspective on the dilemma of newborn vaccination, providing solutions with closed-form expressions that may exhibit periodic or non-periodic behavior. This approach facilitates disease modelers in exploring the potential periodicity of newborn vaccination programs, aiding efforts to prevent recurrent outbreaks.

中文翻译：

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具有潜在周期性行为的新生儿疫苗接种博弈模型

我们探索流行病的复杂动态，考虑到疾病传播、新生儿和死亡率的显着影响。我们采用进化博弈论方法，对新生儿的疫苗接种方面进行建模，并纳入潜在的周期性行为。目标是创建一个引人入胜的模拟，强调及时婴儿疫苗接种的重要性。通过引入周期性元素，游戏增加了复杂性，促进了玩家的参与和对疫苗接种计划的认识。与专注于成人疫苗行为的传统干预博弈模型相比，我们的方法认识到新生儿疫苗接种带来的独特挑战。我们通过开发广义区室模型、适应感染持续时间分布并准确捕获周期性和非周期性疾病轨迹来解决现有模型的局限性。结果表明，新生儿疫苗计划的更高功效有可能根除这种疾病，但更高的功效和成本可能会阻碍疫苗接种。动机成本的增加可以提高疫苗接种率，但不会影响流行病的规模，而成本的降低则可以稳定疫苗接种率。降低疫苗成本需要增加政府投资以消除犹豫。然而，功效降低和积极性降低导致疫苗恐惧分数升高，从而阻碍了参与。我们的工作还为新生儿疫苗接种的困境提供了独特的视角，提供了可能表现出周期性或非周期性行为的封闭式表达式的解决方案。这种方法有助于疾病建模者探索新生儿疫苗接种计划的潜在周期性，有助于防止疾病反复爆发。