In deterministic epidemic models, pathogen extinction in a population is determined by the magnitude of the basic reproduction number R0. In stochastic epidemic models, the probability of pathogen extinction depends on R0, the size of the population and the number of infectious individuals. For example, in the SIS Markov chain epidemic model, if the basic reproduction number R0>1, the population size is large and I(0)=a is small, then a classic result of Whittle (1955) gives an approximation to the probability of pathogen extinction: (1/R0)a. This classic result can be derived from branching process theory. We apply results from multitype Markov branching process theory to generalize this approximation for probability of pathogen extinction to more complex epidemic models with multiple stages, treatment , or multiple populations and to within host models of virus and cell dynamics. Work done in collaboration with Yuan Yuan and Glenn Lahodny.