Spread of disease involving time delay and population dispersal.

An epidemic model with time delay is proposed to incorporate population dispersal between patches, where time delay arises very naturally. We establish a threshold above which the disease is uniformly persistent. Sufficient conditions that lead to the extinction of the disease are obtained. We give sufficient condition for the existence of the positive equilibrium. We also show that when the positive equilibrium exists, it is globally asymptotically stable. Some examples are given to illustrate the effect of population dispersal, time delay and dispersal-related mortality. It is found that a disease may spread when the population migrates in two patches, even though it dies out in some isolated patches. It is also found that population dispersal can reduce the disease spread for strong dispersal rate, large time delay and dispersal-related mortality. [ABSTRACT FROM AUTHOR]