Periodic epidemic outbursts explained by local saturation of clusters

Adding the notion of spatial locality to the susceptible-infected-recovered (or SIR) model, allows to capture local saturation of an epidemic. The resulting minimum model of an epidemic, consisting of five ordinary differential equations with constant model coefficients, reproduces slowly decaying periodic outbursts, as observed in the COVID-19 or Spanish flu epidemic. It is shown that if immunity decays, even slowly, the model yields a fully periodic dynamics.

Automated summary

Adding spatial locality to the SIR model captures local saturation of an epidemic. The resulting minimal epidemic model with five ordinary differential equations and constant coefficients reproduces slowly decaying periodic outbursts observed in COVID-19 or Spanish flu. It is demonstrated that if immunity decays, even slowly, the model exhibits fully periodic dynamics.