标题： 流行病和疫苗模型的通用特性 显示英文标题

标题： Universal features of epidemic and vaccine models

摘要： 在本文中，我们研究了一个包含额外移民过程的随机易感-感染-易感（SIS）流行病模型。在乘性噪声存在的情况下，由环境扰动产生，该模型表现出噪声诱导的转变。分岔图有两个不同的区域，分别是单峰和双峰，在这些区域中，稳态概率分布分别具有一个和两个峰值。除了在两种模式之间的第一类转变外，在尖点处发生临界点转变，该转变属于平均场伊辛 universality 类。该流行病模型与著名的种群遗传学的 Horsthemke-Lefever 模型具有这些特征。在随机环境中，疫苗接种对流行病传播/控制的影响也进行了研究。我们进一步提出了一种一般的疫苗犹豫模型，沿着 Kirman 的蚂蚁模型，其中愿意接种疫苗人口比例的稳态分布由 Beta 分布给出。该分布被证明能很好地拟合新冠疫苗犹豫和接种的数据。我们基于接种人口比例的 Beta 分布，推导出基本再生数的稳态概率分布，这是流行病学中的一个关键参数。我们的研究突出了流行病和疫苗模型与其他动力学模型共有的普遍特性。 显示英文摘要

摘要： In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model exhibits noise-induced transitions. The bifurcation diagram has two distinct regions of unimodality and bimodality in which the steady-state probability distribution has one and two peaks, respectively. Apart from first-order transitions between the two regimes, a critical-point transition occurs at a cusp point with the transition belonging to the mean-field Ising universality class. The epidemic model shares these features with the well-known Horsthemke-Lefever model of population genetics. The effect of vaccination on the spread/containment of the epidemic in a stochastic setting is also studied. We further propose a general vaccine-hesitancy model, along the lines of Kirman's ant model, with the steady-state distribution of the fraction of the vaccine-willing population given by the Beta distribution. The distribution is shown to give a good fit to the COVID-19 data on vaccine hesitancy and vaccination. We derive the steady-state probability distribution of the basic reproduction number, a key parameter in epidemiology, based on a beta-distributed fraction of the vaccinated population. Our study highlights the universal features that epidemic and vaccine models share with other dynamical models.