On SIR-type epidemiological models and population heterogeneity effects

TL;DR

This paper explores the dynamics of SIR-type epidemiological models, revealing a surprising link to Schwarzschild spacetime and analyzing how population heterogeneity and mitigation measures influence disease spread and herd immunity thresholds.

Contribution

It introduces a novel correspondence between epidemic trajectories and spacetime geodesics and models population heterogeneity using gamma distributions to refine herd immunity estimates.

Findings

Discovered a correspondence between epidemic trajectories and Schwarzschild spacetime geodesics.

Modeled population heterogeneity with gamma distributions to assess herd immunity thresholds.

Demonstrated how mitigation measures can be incorporated through model fitting.

Abstract

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.