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Mathematics 2019, 7(2), 157; https://doi.org/10.3390/math7020157

Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

1
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
3
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
*
Author to whom correspondence should be addressed.
Received: 2 December 2018 / Revised: 27 January 2019 / Accepted: 31 January 2019 / Published: 9 February 2019
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Abstract

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4 + T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles. View Full-Text
Keywords: global stability; HIV dynamics; antibody immunity; time delay global stability; HIV dynamics; antibody immunity; time delay
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Elaiw, A.M.; Elnahary, E.K. Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays. Mathematics 2019, 7, 157.

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