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On SIR-type epidemiological models and population heterogeneity effects (2210.11342v1)
Published 20 Oct 2022 in q-bio.PE, gr-qc, hep-th, math.PR, and physics.soc-ph
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.