Assessing intervention strategies for non-homogeneous populations using a closed form formula for R₀

A general stochastic model for susceptible → infective → recovered (SIR) epidemics in non-homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex models. The basic reproduction number R₀, an indication of the probability of an outbreak for homogeneous populations does not indicate the probability of an outbreak for non-homogeneous models anymore, because it changes with the initially infected case. Therefore, we use "individual R₀" that is the expected number of secondary cases for a unique given initially infected individual. Thus, the effectiveness of intervention strategies can be assessed by their capability to reduce individual R₀ values. Also a vaccination plan based on individual R₀ values for fully heterogeneous populations is proposed. It is based on the recursive calculation of individual R₀ values.