Abstract
ABSTRACTTime delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves.
Highlights
Human immunodeficiency virus type 1 (HIV-1) infects CD4+ T cells, a substantial component of the immune system, and the infection goes through three distinct stages: primary infection, asymptomatic stage, and acquired immunodeficiency syndrome (AIDS)
This paper investigates the asymptotical behaviour of the solutions of delay differential equation systems that are used to study HIV infection dynamics
One is the time between initial cell infection and the establishment of latent infection, and the other is the time between viral entry into cell and viral production in productively infected cells
Summary
Human immunodeficiency virus type 1 (HIV-1) infects CD4+ T cells, a substantial component of the immune system, and the infection goes through three distinct stages (see review in [31]): primary infection, asymptomatic stage, and acquired immunodeficiency syndrome (AIDS). The primary infection stage lasts a few weeks during which the viral load in blood increases rapidly to the peak level, followed by decline to a steady state. A high level of viral infection stimulates the development of adaptive immune responses, including CD8+ T cells, which can kill infected cells [55]. Mathematical models have been developed to study the dynamics of virions and CD4+ T cells during infection, the influence of antiretroviral therapy, the emergence of drug resistance, immune responses, and low viral load persistence in patients receiving prolonged antiretroviral therapy (see reviews in [34,35,36, 43]). A time delay representing the time between cell infection and viral production has been incorporated into models to study its influence on virus dynamics. We will use the method developed by Gu et al [16] to determine the stability crossing curves for the infected steady state of the model when both delays are positive
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