Renormalisation Group Methods for Effective Epidemiological Models
arxiv(2024)
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.
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