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Analysis of the dynamics of a delayed HIV pathogenesis model. (English) Zbl 1185.92062
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.

92C50Medical applications of mathematical biology
34K20Stability theory of functional-differential equations
34K18Bifurcation theory of functional differential equations
34K60Qualitative investigation and simulation of models
65C20Models (numerical methods)
Full Text: DOI
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