标题： 重正化群方法用于有效的流行病学模型 显示英文标题

标题： Renormalisation Group Methods for Effective Epidemiological Models

摘要： 流行病学模型描述了人群中传染病的传播。 这些模型以多种不同方式捕获疾病在个体间传播的微观细节，同时预测整个人群的状态。 然而，所考虑的具体模型的类型和结构通常取决于所研究人群的规模。 为了分析这种影响，我们研究了一组与空间和时间相关的有效流行病学模型，这些模型通过尺度变换相互关联。 受到扩散过程类似处理的启发，我们在基本微分方程及其解的层面上将后者解释为重正化群变换。 我们证明，在大尺度极限下，感染过程的微观细节变得无关紧要，除了一个简单的实数，它在基本仓室模型中扮演着感染率的角色。 显示英文摘要

摘要： Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state of the entirety of the population. However, the type and structure of the specific model considered typically depend on the size of the population under consideration. To analyse this effect, we study a family of effective epidemiological models in space and time that are related to each other through scaling transformations. Inspired by a similar treatment of diffusion processes, we interpret the latter as renormalisation group transformations, both at the level of the underlying differential equations and their solutions. We show that in the large scale limit, the microscopic details of the infection process become irrelevant, safe for a simple real number, which plays the role of the infection rate in a basic compartmental model.