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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 4: 919-927. doi: 10.3934/mbe.2014.11.919
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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
  • Received: 01 August 2013 Accepted: 29 June 2018 Published: 01 March 2014

  • MSC : 92D30.

  • Due to their very high replication and mutation rates, RNA virusescan serve as an excellent testing model for verifying hypothesis andaddressing questions in evolutionary biology.In this paper, we suggest a simple deterministic mathematical modelof the within-host viral dynamics, where a possibility for random mutations incorporates.This model assumes a continuous distribution of viral strainsin a one-dimensional phenotype space where random mutations aremodelled by Brownian motion (that is, by diffusion).Numerical simulations show that randommutations combined with competition for a resource result in evolutiontowards higher Darwinian fitness: a stable pulse traveling waveof evolution, moving towards higher levels of fitness,is formed in the phenotype space.The advantage of this model, compared with the previously constructedmodels, is that this model is mechanistic and is based on commonlyaccepted model of virus dynamics within a host, and thus it allowsan incorporation of features of the real-life host-virus system such as immuneresponse, antiviral therapy, etc.

    Citation: Andrei Korobeinikov, Conor Dempsey. A continuous phenotype space model of RNA virus evolution within a host[J]. Mathematical Biosciences and Engineering, 2014, 11(4): 919-927. doi: 10.3934/mbe.2014.11.919

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  • Due to their very high replication and mutation rates, RNA virusescan serve as an excellent testing model for verifying hypothesis andaddressing questions in evolutionary biology.In this paper, we suggest a simple deterministic mathematical modelof the within-host viral dynamics, where a possibility for random mutations incorporates.This model assumes a continuous distribution of viral strainsin a one-dimensional phenotype space where random mutations aremodelled by Brownian motion (that is, by diffusion).Numerical simulations show that randommutations combined with competition for a resource result in evolutiontowards higher Darwinian fitness: a stable pulse traveling waveof evolution, moving towards higher levels of fitness,is formed in the phenotype space.The advantage of this model, compared with the previously constructedmodels, is that this model is mechanistic and is based on commonlyaccepted model of virus dynamics within a host, and thus it allowsan incorporation of features of the real-life host-virus system such as immuneresponse, antiviral therapy, etc.


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