Advances in Applied Probability

Conditional distributions and waiting times in multitype branching processes

H. K. Alexander

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Abstract

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the non\-appearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

Article information

Source
Adv. in Appl. Probab., Volume 45, Number 3 (2013), 692-718.

Dates
First available in Project Euclid: 30 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1377868535

Digital Object Identifier
doi:10.1239/aap/1377868535

Mathematical Reviews number (MathSciNet)
MR3102468

Zentralblatt MATH identifier
1276.92081

Subjects
Primary: 60G99: None of the above, but in this section
Secondary: 92D15: Problems related to evolution 92D30: Epidemiology

Keywords
Multitype branching process probability generating function waiting time escape mutant evolutionary biology epidemiology

Citation

Alexander, H. K. Conditional distributions and waiting times in multitype branching processes. Adv. in Appl. Probab. 45 (2013), no. 3, 692--718. doi:10.1239/aap/1377868535. https://projecteuclid.org/euclid.aap/1377868535


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