A branching model for the spread of infectious animal diseases in varying environments

This paper is concerned with a stochastic model, describing out-breaks of infectious diseases that have potentially great animal or hu-man health consequences, and which can result in such severe eco-nomic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environ-ment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environ-ment. With this branching process, we estimate the probability of extinction and the expected number of infected individuals for dier-ent control measures. We also use this branching process to calculate the generating function of the number of infected individuals at any given moment. The model and methods are designed using important infections of farmed animals, such as classical swine fever, foot-and-mouth disease and avian in uenza as motivating examples, but have a wider application, for example to emerging human infections that lead to strict quarantine of cases and suspected cases (e.g. SARS) and contact and movement restrictions