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Coexistence and Noncoexistence of Markovian Viruses and their Hosts

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Jakob E. Björnberg  and
Erik I. Broman
Jakob E. Björnberg*
Affiliation:
Uppsala University
Erik I. Broman*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, Uppsala, 751 06, Sweden.
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, Uppsala, 751 06, Sweden.
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Abstract

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Examining possibilities for the coexistence of two competing populations is a classic problem which dates back to the earliest ‘predator-prey’ models. In this paper we study this problem in the context of a model introduced in Björnberg et al. (2012) for the spread of a virus infection in a population of healthy cells. The infected cells may be seen as a population of ‘predators’ and the healthy cells as a population of ‘prey’. We show that, depending on the parameters defining the model, there may or may not be coexistence of the two populations, and we give precise criteria for this.

Keywords

Coexistencebranching processinteracting branching process

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 191 - 208
Copyright
© Applied Probability Trust 

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