### 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.

Original language | English (US) |
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Pages (from-to) | 155-166 |

Number of pages | 12 |

Journal | Markov Processes and Related Fields |

Volume | 20 |

Issue number | 1 |

State | Published - 2014 |

### Keywords

- Influenza
- Mutation
- Phylogenetic tree
- Stochastic model

### ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics

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## Cite this

Cox, J. T., & Schinazi, R. B. (2014). A stochastic model for the evolution of the influenza virus.

*Markov Processes and Related Fields*,*20*(1), 155-166.