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Mathematical Medicine and Biology Advance Access originally published online on November 17, 2008
Mathematical Medicine and Biology 2008 25(4):285-322; doi:10.1093/imammb/dqn023
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Multistrain virus dynamics with mutations: a global analysis

Patrick De Leenheer{dagger} and Sergei S. Pilyugin{ddagger}

Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA

{dagger} Corresponding author. Email: deleenhe{at}math.ufl.edu

{ddagger} Email: pilyugin{at}math.ufl.edu

Received on March 22, 2007. Revised on September 11, 2007. Accepted on October 7, 2007.

We consider within-host virus models with n ≥ 2 strains and allow mutation between the strains. If there is no mutation, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For small perturbations, this steady state persists, perhaps with small concentrations of some or all other strains, depending on the connectivity of the graph describing all possible mutations. Moreover, using a perturbation result due to Smith & Waltman (1999), we show that this steady state also preserves global stability.

Keywords: within-host virus models; mutations; quasispecies; global stability; Lyapunov function

To our mentor and good friend Hal Smith on the occasion of his 60th birthday


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