Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. (English) Zbl 1260.92065

Liu, Shengqiang; Wang, Lin

Math. Biosci. Eng. 7, No. 3, 675-685 (2010).

Summary: Global stability is analyzed for a general mathematical model of HIV-1 pathogenesis proposed by P.W. Nelson and A.S. Perelson [Math. Biosci. 179, No. 1, 73–94 (2002; Zbl 0992.92035)]. The general model includes two distributed intracellular delays and a combination therapy with a reverse transcriptase inhibitor and a protease inhibitor. It is shown that the model exhibits a threshold dynamics: if the basic reproduction number is less than or equal to one, then the HIV-1 infection is cleared from the T-cell population; whereas if the basic reproduction number is larger than one, then the HIV-1 infection persists and the viral concentration maintains at a constant level.

MSC:

92C60	Medical epidemiology
34K20	Stability theory of functional-differential equations

Keywords:

HIV-1; steady state; Lyapunov functionals

Citations:

Zbl 0992.92035