Allen L.J.S. Stochastic Population and Epidemic Models: Persistence and Extinction

Springer, 2015. — 55 p. — (Mathematical Biosciences Institute Lecture Series. Volume 1: Stochastics in Biological Systems). — ISBN: 978-3-319-21553-2.This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MatLAB programs for simulating stochastic sample paths are provided in an Appendix.Continuous-Time and Discrete-State Branching Processes
Applications of Single-Type Branching Processes
Applications of Multi-Type Branching Processes
Continuous-Time and Continuous-State Branching Processes