An epidemic model is studied to understand the effect
of a population dispersal on the spread of a disease in two patches.
Under the assumption that the dispersal of infectious individuals
barred, it is found that susceptive dispersal may cause the spread
of the disease in one patch even though the disease dies out in
each isolated patch.
For the case where the disease spreads in each
isolated patch, it is shown that suitable susceptive dispersal
can lead to the extinction of
the disease in one patch.