Stochastic Multigroup Epidemic Models: Duration and Final Size

Abstract

The epidemic duration, the final epidemic size, and the probability of an outbreak are studied in stochastic multigroup epidemic models. Two models are considered, where the transmission rate for each group either depends on the infectious individuals or on the susceptible individuals, referred to as Model 1 and Model 2, respectively. Such models are applicable to emerging and re-emerging infectious diseases. Applying a multitype branching process approximation, it is shown for Model 1 that an outbreak is dependent primarily on group reproduction numbers, whereas for Model 2, this dependence is due to group recovery rates. The probability distributions for epidemic duration and for final size are a mixture of two distributions, that depend on whether an outbreak occurs. Given there is an outbreak, it is shown that the mean final size of the stochastic multigroup model agrees well with the final size obtained from the underlying deterministic model. These methods can be extended to more general stochastic multigroup models and to other stochastic epidemic models with multiple stages, patches, hosts, or pathogens.