Abstract
The study of branching processes began in the mid 19th century with the work of Bienaymé, Galton, and Watson [10, 23, 39]. Galton and Watson’s original problem was to study the extinction of family surnames. They formalized the problem using probability generating functions. This first application employed discrete-time branching processes. Continuous-time branching process theory is closely related to discrete-time theory. In this chapter, we summarize the basic theory for continuous-time and discrete-state branching processes for single-type and multi-type processes. This theory is used to estimate population extinction (absorption) in two examples, a birth-death model and a birth-death-dispersal model. In later chapters, the branching process theory, developed in this chapter, is applied to some classic population and epidemic models to predict species invasions or outbreaks in more complex settings. Further mathematical details about the theory and additional biological examples can be found in the references (e.g., [7, 14, 20, 23, 24, 32]).
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Allen, L.J.S. (2015). Continuous-Time and Discrete-State Branching Processes. In: Stochastic Population and Epidemic Models. Mathematical Biosciences Institute Lecture Series(), vol 1.3. Springer, Cham. https://doi.org/10.1007/978-3-319-21554-9_1
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DOI: https://doi.org/10.1007/978-3-319-21554-9_1
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