Two applications of multi-type branching processes to epidemic models are presented. The first application is to an SEIR epidemic model and the second application is to the same epidemic model but with dispersal. The SEIR epidemic is modeled as a two-type branching process. Occurrence of an outbreak depends on the number of exposed and infectious individuals. It is shown that the offspring pgfs for the exposed and infectious populations lead to an explicit formula for the probability of an outbreak.
Applications of Multi-Type Branching Processes