The Probability of Extinction of a Dynamic Epidemic Model

We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals can move between populations and infectives can only make infections with members of their current population. Attention is focussed upon the effect of the distribution of the infectious period on the probability that the epidemic goes extinction in the limit as the total population size N → ∞ . Infectious periods comprising the sum of exponential random variables are considered. For this wide class of infectious periods it is shown that the probability of extinction of the epidemic process for a fixed mean infectious period is maximised by an exponentially distributed infectious period, and minimised by an infectious period of constant length.