The basic reproduction number, R0, in structured populations

•A straightforward approach for deriving R0 for SIR and SIS epidemics in structured populations.•Simple recursive formula for the mean reproduction matrix in terms of transition events.•The calculation of R0 coincides with that derived through a branching process construction for SIR household epidemics. In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, R0, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both SIR and SIS epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for R0 agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number.