The time-delay effect of a metapopulation

The simplified incidence function model with small delay time was employed to study the stability and mean extinction time of a metapopulation. By numerically computing the mean passage time and analyzing the stationary probability distribution function of the metapopulation，we found that：1) As delay time increases，the probability that pathe are occupied by a metapopulation decreases; 2) As delay time increases，the mean extinction time of a metapopulation decreases.