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A Stochastic Model for Virus Growth in a Cell Population

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

J. E. Björnberg ,
T. Britton ,
E. I. Broman  and
E. Natan
J. E. Björnberg*
Affiliation:
Uppsala University
T. Britton*
Affiliation:
Stockholm University
E. I. Broman*
Affiliation:
Uppsala University
E. Natan*
Affiliation:
University of Cambridge
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden.
∗∗ Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden.
∗∗∗∗ Postal address: MRC Laboratory of Molecular Biology, University of Cambridge, Francis Crick Avenue, Cambridge CB2 0QH, UK.
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Abstract

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In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter λ which quantifies the ‘aggressiveness’ of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to λ = 0. This is in agreement with experimental data about real viruses.

Keywords

Branching processinteracting branching processmodel for virus growth

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J28: Applications of continuous-time Markov processes on discrete state spaces 92D15: Problems related to evolution
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 599 - 612
Copyright
© Applied Probability Trust 

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