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

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Abstract

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.

Cite this work

Researchers should cite this work as follows:

  • Brian Winkel (2017), "Mathematical analysis of delay differential equation models of HIV-1 infection," https://simiode.org/resources/3289.

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