  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.
