Slow decay of infection in the inhomogeneous SIR model

TL;DR

This study investigates how spatial inhomogeneity in infection rates affects the decay of infections in the SIR model, revealing that infections can persist longer than predicted by traditional models, especially in hot spots.

Contribution

It introduces numerical simulations of the inhomogeneous SIR model across multiple dimensions, highlighting the slow decay of infections in inhomogeneous environments.

Findings

Infection decay is significantly slower in inhomogeneous systems.

Localized hot spots sustain infections longer.

Complete disease eradication is more difficult in inhomogeneous settings.

Abstract

The SIR model with spatially inhomogeneous infection rate is studied with numerical simulations in one, two, and three dimensions, considering the case that the infection spreads inhomogeneously in densely populated regions or hot spots. We find that the total population of infection decays very slowly in the inhomogeneous systems in some cases, in contrast to the exponential decay of the infected population I(t) in the SIR model of the ordinary differential equation. The slow decay of the infected population suggests that the infection is locally maintained for long and it is difficult for the disease to disappear completely.