On SIR-type epidemiological models and population heterogeneity effects

In this paper we elaborate on homogeneous and heterogeneous SIR-type epidemiological models. We find an unexpected correspondence between the epidemic trajectory of a transmissible disease in a homogeneous SIR-type model and radial null geodesics in the Schwarzschild spacetime. We also discuss modeling of population heterogeneity effects by considering both a one-and two-parameter gamma-distributed function for the initial susceptibility distribution, and deriving the associated herd immunity threshold. We furthermore describe how mitigation measures can be taken into account by model fitting. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we discuss homogeneous and heterogeneous SIR-type epidemiological models. Surprisingly, we discover a correspondence between the epidemic trajectory in a homogeneous SIR-type model and radial null geodesics in the Schwarzschild spacetime. We also explore population heterogeneity effects by examining the initial susceptibility distribution and deriving the herd immunity threshold, and propose a method to incorporate mitigation measures through model fitting.