A Stochastic Model for Virus Growth in a Cell Population

This work introduces 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 on and duplicate, or else by multiplying in large numbers within the host cell, causing the host cell to burst thereby letting the viruses enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular 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