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.

翻译：流行病学模型描述了传染病在人群中的传播过程。这些模型以多种不同方式捕捉疾病在个体间传播的微观细节，同时对整个群体的状态进行预测。然而，所采用的具体模型类型和结构通常取决于所研究的人口规模。为了分析这一效应，我们研究了一系列时空中的有效流行病模型，这些模型通过尺度变换相互关联。受扩散过程类似处理方式的启发，我们将后者解释为重正化群变换，既在底层微分方程层面，也在其解层面。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，仅剩一个简单的实数起核心作用，该实数在基础舱室模型中扮演感染率角色。