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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.
These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA.
Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in theDepartment of Mathematics and Statistics at Texas Tech University, USA.
List of contents
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.-MatLaB Programs.
About the author
Linda J. S. Allen is a Professor in the Department of Mathematics and Statistics at Texas Tech University. Allen's primary research interest is mathematical modeling in biology. She formulates and analyzes deterministic and stochastic models in describing population, epidemic, viral and immune-system dynamics.
Summary
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.
These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA.
Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in theDepartment of Mathematics and Statistics at Texas Tech University, USA.
Additional text
“The readers will certainly appreciate the quality of a text written in a very clear way, well-organized and with high pedagogical standard. … Stochastic Population and Epidemic Models (Persistence and Extinction) is indeed a short, but complete, manual for the study of stochastic population and epidemic models indispensable for graduate students, for whom it was thought, but also accessible to many more audiences: professionals or simply curious on these subjects.” (Manuel Alberto M. Ferreira, Acta Scientiae et Intellectus, Vol. 3 (2), 2017)
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"The readers will certainly appreciate the quality of a text written in a very clear way, well-organized and with high pedagogical standard. ... Stochastic Population and Epidemic Models (Persistence and Extinction) is indeed a short, but complete, manual for the study of stochastic population and epidemic models indispensable for graduate students, for whom it was thought, but also accessible to many more audiences: professionals or simply curious on these subjects." (Manuel Alberto M. Ferreira, Acta Scientiae et Intellectus, Vol. 3 (2), 2017)
