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2014, 11(4): 919-927. doi: 10.3934/mbe.2014.11.919

## A continuous phenotype space model of RNA virus evolution within a host

 1 Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona 2 Department of Neuroscience, Columbia University, 40 Haven Avenue, New York, NY 10032, United States

Received  August 2013 Revised  October 2013 Published  March 2014

Due to their very high replication and mutation rates, RNA viruses can serve as an excellent testing model for verifying hypothesis and addressing questions in evolutionary biology. In this paper, we suggest a simple deterministic mathematical model of the within-host viral dynamics, where a possibility for random mutations incorporates. This model assumes a continuous distribution of viral strains in a one-dimensional phenotype space where random mutations are modelled by Brownian motion (that is, by diffusion). Numerical simulations show that random mutations combined with competition for a resource result in evolution towards higher Darwinian fitness: a stable pulse traveling wave of evolution, moving towards higher levels of fitness, is formed in the phenotype space. The advantage of this model, compared with the previously constructed models, is that this model is mechanistic and is based on commonly accepted model of virus dynamics within a host, and thus it allows an incorporation of features of the real-life host-virus system such as immune response, antiviral therapy, etc.
Citation: Andrei Korobeinikov, Conor Dempsey. A continuous phenotype space model of RNA virus evolution within a host. Mathematical Biosciences & Engineering, 2014, 11 (4) : 919-927. doi: 10.3934/mbe.2014.11.919
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