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Mathematical Medicine and Biology Advance Access originally published online on May 25, 2008
Mathematical Medicine and Biology 2008 25(2):99-112; doi:10.1093/imammb/dqm010
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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.

Impact of delays in cell infection and virus production on HIV-1 dynamics

Huiyan Zhu

School of Mathematics and Physics, Nanhua University, Hengyang, Hunan 421001, People's Republic of China

Xingfu Zou{dagger}

Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada

{dagger} Email: xzou{at}uwo.ca

Received on April 18, 2007. Revised on November 14, 2007. Accepted on November 20, 2007.

Analysed is a mathematical model for HIV-1 infection with two delays accounting, respectively, for (i) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and (ii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproduction number Formula is identified and its threshold property is discussed: the uninfected steady state is proved to be globally asymptotically stable if Formula and unstable if Formula . In the latter case, an infected steady state occurs and is proved to be locally asymptotically stable. The formula for shows that increasing either of the two delays will decrease Formula . This may suggest a new direction for new drugs—drugs that can prolong the latent periFormula od and/or slow down the virus production process.

Keywords: HIV-1; cells; virus; delays; stability


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