Thresholds for Extinction in Stochastic Models of Infectious Diseases: Importance of Time and Location

Linda Allen (April 7, 2014)

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Abstract

Relations between Markov chain models and differential equation models for infectious diseases near the infection-free state are derived. Approximation of the Markov chain model by a multitype branching process leads to an estimate of the probability of disease extinction. We summarize some extinction results for multi-patch, multi-group, and multi-stage models of infectious diseases for epidemics and within-host models. The successful invasion of a pathogen often depends on the conditions of the environment at a specific time and location.