Abstract

Citation

Researchers should cite this work as follows:

• Nelson, P. W. (2023). 2002-Nelson-Perelson-Mathematical analysis of delay differential equations models of HIV-1 infection. SIMIODE, QUBES Educational Resources. doi:10.25334/1EAX-7J12

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Nelson, P. W. and A. S. Perelson. 2002. Mathematical analysis of delay differential equations models of HIV-1 infection. Mathematical Biosciences. 179: 73-94.

See http://math.lsa.umich.edu/~pwn/MBiosci2.pdf . Accessed 27 March 2023.

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 fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of delta. We also provide some general results on the stability of non-linear delay differential equation infection models.

Keywords: delay, differential equation, model, HIV, infection, T cell,