An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells
Mathematical models of HIV-1 infection can help interpretdrug treatment experiments and improve our understanding of the interplay between HIV-1and the immune system. We develop and analyze an age-structured model of HIV-1 infection thatallows for variations in the death rate of productively infec...
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AIMS Press
2004-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.267 |
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| author | Patrick W. Nelson Michael A. Gilchrist Daniel Coombs James M. Hyman Alan S. Perelson |
| author_facet | Patrick W. Nelson Michael A. Gilchrist Daniel Coombs James M. Hyman Alan S. Perelson |
| author_sort | Patrick W. Nelson |
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| description | Mathematical models of HIV-1 infection can help interpretdrug treatment experiments and improve our understanding of the interplay between HIV-1and the immune system. We develop and analyze an age-structured model of HIV-1 infection thatallows for variations in the death rate of productively infected T cellsand the production rate of viral particles as a function of thelength of time a T cell has been infected. We show that this model is a generalization ofthe standard differential equation and of delay models previously used to describeHIV-1 infection, and provides a means for exploring fundamental issuesof viral production and death. We show that the model has uninfected andinfected steady states, linked by a transcritical bifurcation. We performa local stability analysis of the nontrivialequilibrium solution and provide a general stability condition for models withage structure. We then use numerical methods to study solutions of our model focusing on theanalysis of primary HIV infection. We show that the time to reach peak viral levels in theblood depends not only on initial conditions but also on the way in which viral productionramps up. If viral production ramps up slowly, we find that the time to peak viral loadis delayed compared to results obtained using the standard (constant viral production)model of HIV infection. We find that data on viral load changing over time is insufficientto identify the functions specifying the dependence of theviral production rate or infected cell death rate on infected cell age. These functions mustbe determined through new quantitative experiments. |
| format | Article |
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| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-06-01 |
| publisher | AIMS Press |
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| spelling | doaj-art-7fa64c3bb8d8418a922823af2359d7302025-01-24T01:46:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-06-011226728810.3934/mbe.2004.1.267An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected CellsPatrick W. Nelson0Michael A. Gilchrist1Daniel Coombs2James M. Hyman3Alan S. Perelson4Department of Mathematics, University of Michigan, 5860 E. Hall, Ann Arbor, MI 48109Department of Biology, University of New Mexico, Albuquerque, NM 87131Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2Mathematical Modeling and Analysis, T-7, Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545Theoretical Division T-10, Los Alamos National Laboratory, Los Alamos, NM 87545Mathematical models of HIV-1 infection can help interpretdrug treatment experiments and improve our understanding of the interplay between HIV-1and the immune system. We develop and analyze an age-structured model of HIV-1 infection thatallows for variations in the death rate of productively infected T cellsand the production rate of viral particles as a function of thelength of time a T cell has been infected. We show that this model is a generalization ofthe standard differential equation and of delay models previously used to describeHIV-1 infection, and provides a means for exploring fundamental issuesof viral production and death. We show that the model has uninfected andinfected steady states, linked by a transcritical bifurcation. We performa local stability analysis of the nontrivialequilibrium solution and provide a general stability condition for models withage structure. We then use numerical methods to study solutions of our model focusing on theanalysis of primary HIV infection. We show that the time to reach peak viral levels in theblood depends not only on initial conditions but also on the way in which viral productionramps up. If viral production ramps up slowly, we find that the time to peak viral loadis delayed compared to results obtained using the standard (constant viral production)model of HIV infection. We find that data on viral load changing over time is insufficientto identify the functions specifying the dependence of theviral production rate or infected cell death rate on infected cell age. These functions mustbe determined through new quantitative experiments.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.267and production rates.age-structured modelhivvariable death |
| spellingShingle | Patrick W. Nelson Michael A. Gilchrist Daniel Coombs James M. Hyman Alan S. Perelson An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells Mathematical Biosciences and Engineering and production rates. age-structured model hiv variable death |
| title | An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells |
| title_full | An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells |
| title_fullStr | An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells |
| title_full_unstemmed | An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells |
| title_short | An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells |
| title_sort | age structured model of hiv infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells |
| topic | and production rates. age-structured model hiv variable death |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.267 |
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