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Linda Allen


Speaker: Linda Allen
Title: Predicting Population Extinction and Disease Outbreaks with Branching Processes
Affiliation: Texas Tech University
Date: Friday, April 3, 2015
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Thresholds for population or disease extinction provide essential information for control, eradication or management of populations and diseases. Continuous-time Markov chain models and their branching process approximation near the extinction state are formulated for population and epidemic models. The stochastic formulations are based on a deterministic framework which provides useful comparisons with the stochastic models. Although it is well-known that the large population limit of a Markov chain model often leads to a deterministic system of ordinary differential equations, when population sizes are small, the stochastic model, with discrete numbers of individuals, must be applied to study extinction. Some of the theory for branching processes is summarized, then applied to predict the probability of population extinction or of a disease outbreak in some classic population and epidemic models. The usefulness of the branching process is demonstrated in several new applications, including a species invasion problem and in disease control with dispersal between locations with different health care.