Abstract

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Researchers should cite this work as follows:

• Yang, J. (2023). 2008-Yang-EtAl-Differential Equation Model of HIV Infection of CD T-Cells with Delay . SIMIODE, QUBES Educational Resources. doi:10.25334/97WB-4633

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Yang, Junyuan , Xiaoyan Wang, and Fengqin Zhang. 2008. A Differential Equation Model of HIV Infection of CD T-Cells with Delay. Volume 2008. Article ID 903678.

See https://www.hindawi.com/journals/ddns/2008/903678/ . Accessed on 27 March 2023.

Abstract: An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0<1. If R0<1, the disease-free equilibrium is asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region. In the DDE model, the delay stands for the incubation time. We prove the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the virus-to-healthy cells transmission term candestabilize the system, and periodic solutions can arise through Hopf bifurcation.