## Journal of Applied Probability

### A stochastic model for virus growth in a cell population

#### Abstract

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.

#### Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 599-612.

Dates
First available in Project Euclid: 5 September 2014

https://projecteuclid.org/euclid.jap/1409932661

Digital Object Identifier
doi:10.1239/jap/1409932661

Mathematical Reviews number (MathSciNet)
MR3256214

Zentralblatt MATH identifier
1305.60083

#### Citation

Björnberg, J. E.; Britton, T.; Broman, E. I.; Natan, E. A stochastic model for virus growth in a cell population. J. Appl. Probab. 51 (2014), no. 3, 599--612. doi:10.1239/jap/1409932661. https://projecteuclid.org/euclid.jap/1409932661

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