The basic reproduction number and the probability of extinction for a dynamic epidemic model.

We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R₀, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N→∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R₀ and the probability of extinction. However, it is shown that for n=2, the basic reproduction number, R₀, is maximised by a constant length infectious period and is decreasing in ς, the speed of movement between the two populations.