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Zbl 1185.92062
Hu, Zhixing; Liu, Xiangdong; Wang, Hui; Ma, Wanbiao
Analysis of the dynamics of a delayed HIV pathogenesis model. (English)
[J] J. Comput. Appl. Math. 234, No. 2, 461-476 (2010). ISSN 0377-0427

Summary: Considering full logistic proliferation of CD4$^{+}$ T cells, we study an HIV pathogenesis model with antiretroviral therapy and HIV replication time. We first analyze the existence and stability of the equilibrium, and then investigate the effect of the time delay on the stability of the infected steady state. Sufficient conditions are given to ensure that the infected steady state is asymptotically stable for all delays. Furthermore, we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold, and investigate the existence of Hopf bifurcation by using a delay $\tau $ as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the main results.

MSC 2000:: *92C50 Medical appl. of mathematical biology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional differential equations
34K60 Applications of functional-differential equations
65C20 Models (numerical methods)

Keywords: stability; HIV; CD4$^{+}$ T cells; Hopf bifurcation; antiretroviral therapy; delay

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Zentralblatt MATH Berlin [Germany]