A threshold limit theorem for a multitype epidemic model

The asymptotic final size distribution of a multitype Martin-Löf process, a discrete-time SIR model for the spread of an infectious disease in a closed multitype population, is derived for the case of large total population size. When all subgroups are of comparable size and the infection pattern is irreducible, a threshold behavior is obtained, and the asymptomatic distributions for small and large outbreaks can be found. As an important corollary we get a threshold limit theorem for a class of continuous-time SIR models with several types.