TY - JOUR AU - Elaiw, A. M. AU - Elnahary, E. Kh. PY - 2018 TI - Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART JO - Journal of Mathematics and Computer Science SP - 430--452 VL - 18 IS - 4 AB - 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. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.018.04.05 DO - 10.22436/jmcs.018.04.05 ID - Elaiw2018 ER - TY - JOUR TI - The challenge of viral reservoirs in HIV-1 infection AU - J. N. Blankson AU - D. Persaud AU - R. F. Siliciano JO - Annu. Rev. Med. PY - 2002 DA - 2002// VL - 53 ID - Blankson2002 ER - TY - JOUR TI - Global stability for an HIV-1 infection model including an eclipse stage of infected cells AU - B. Buonomo AU - C. Vargas-De-León JO - J. Math. Anal. Appl. PY - 2012 DA - 2012// VL - 385 ID - Buonomo2012 ER - TY - JOUR TI - HIV-1 infection and low steady state viral loads AU - D. S. Callaway AU - A. S. Perelson JO - Bull. Math. Biol. 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