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arXiv · 1302.2362

A stochastic model for the evolution of the influenza virus

J. T. Cox·R. B. Schinazi
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Abstract

Consider a birth and death chain to model the number of types of a given virus. Each type gives birth to a new type at rate $λ$ and dies at rate 1. Each type is also assigned a fitness. When a death occurs either the least fit type dies (with probability $1-r$) or we kill a type at random (with probability $r$). We show that this random killing has a large effect (for any $r>0$) on the behavior of the model when $λ<1$. The behavior of the model with $r>0$ and $λ<1$ is consistent with features of the phylogenetic tree of influenza.

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J. T. Cox, R. B. Schinazi. 2013-02-10. A stochastic model for the evolution of the influenza virus. https://arxiv.org/abs/1302.2362

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