Renormalisation group methods for effective epidemiological models

Stefan Hohenegger and Francesco Sannino

Physica A: Statistical Mechanics and its Applications, 2024, vol. 656, issue C

Abstract: 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.

Keywords: Epidemiology; Renormalisation Group; Scaling (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:656:y:2024:i:c:s037843712400709x

DOI: 10.1016/j.physa.2024.130200

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