The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An ‘environment’ in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here ‘term-time forcing’ refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {Λ(t)}t≥0. Threshold conditions in terms of R⋆ are obtained, such that R⋆>1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen.

Seasonal forcing is identified as a key pattern generating mechanism in an epidemic model of rabies dispersal. We reduce an established individual-based high-detail modeldown to a deterministic conceptual model. The characteristic wave pattern characterized byhigh densities of infected individuals is maintained throughout the reduction process. In ourmodel it is evident that seasonal forcing is the dominant factor that drives pattern formation.In particular we show that seasonal forcing can cause splitting of epidemic wave fronts.