# Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART

Volume 18, Issue 4, pp 430--452 Publication Date: December 12, 2018       Article History
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### Authors

A. M. Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. E. Kh. Elnahary - Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt.

### Abstract

We investigate a general HIV infection model with three types of infected cells: latently infected cells, long-lived productively infected cells, and short-lived productively infected cells. We consider two kinds of target cells: CD4$^{+}$ T cells and macrophages. We incorporate three discrete time delays into the model. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The HIV-target incidence rate, production/proliferation, and removal rates of the cells and HIV are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive two threshold parameters which determine the stability of the three steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.

### Keywords

• HIV infection
• humoral immune response
• latency
• viral reservoirs

•  34D20
•  34D23
•  37N25

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