  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.
