arXiv subjects

R. B. Schinazi

Publications and source records attributed to R. B. Schinazi.

2 recordsLinked to original sources

arXiv2013

A stochastic model for the evolution of the influenza virus

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.

math.PR↗

arXiv2009

A stochastic model for phylogenetic trees

We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampled from a fixed distribution. At each death the type with the smallest fitness is killed. We show that if the birth (i.e. mutation) rate is subcritical we get a phylogenetic tree consistent with an influenza tree (few types at any given time and one dominating type lasting a long time). When the birth rate is supercritical we get a phylogenetic tree consistent with an HIV tree (many types at any given time, none lasting very long).

math.PR↗