Discrete stochastic metapopulation model with arbitrarily distributed infectious period.

In this study, a stochastic discrete-time model is developed to study the spread of an infectious disease in an n-patch environment. The model includes an arbitrary distribution of the (random) infectious period T, and the results are used to investigate how the distribution of T may influence the model outcomes. General results are applied to specific distributions including Geometric, Negative Binomial, Poisson and Uniform. The model outcomes are contrasted both numerically and analytically by comparing the corresponding basic reproduction numbers R0 and probability of a minor epidemic (or probability of disease extinction) P0. It is shown analytically that for n = 2 the reproduction numbers corresponding to different distributions of T can be ordered based on the probability generating function ϕT of T. In addition, numerical simulations are carried out to examine the final epidemic size F and duration of the epidemic D of a two-patch model.