Slow decay of infection in the inhomogeneous susceptible-infected-recovered model

The susceptible-infected-recovered (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.