Mathematical analysis of delay differential equation models of HIV-1 infection

By Brian Winkel


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Nelson, Patrick W. and Alan S. Perelson. 2002. Mathematical analysis of delay differential equation models of HIV-1 infection. Mathematical Biosciences. 179: 73–94.

Article Abstract: Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells, d, is increased when data is .t with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of d. We also provide some general results on the stability of non-linear delay differential equation infection models.

Keywords: HIV-1; Delay differential equations; combination antiviral therapy; T cells; stability analysis.

The paper offers a good literature survey of use of delay differential equations in modeling biological phenomena and then moves to modification of a nonlinear system of differential equations for various types of cells in the HIV-1 infection process. A delay model is offered with full stability analysis showing for reasonable delays the stability of the delay system is the same as that of the non-delay system. The authors offer parameter estimation for several patients’ data and the claims of the abstract are justified in the details of the analyses.

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  • Brian Winkel (2017), "Mathematical analysis of delay differential equation models of HIV-1 infection,"

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