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Oscillatory viral dynamics in a delayed HIV pathogenesis model. (English) Zbl 1168.92031
Summary: We consider an HIV pathogenesis model incorporating antiretroviral therapy and HIV replication time. We investigate the existence and stability of equilibria, as well as Hopf bifurcations to sustained oscillations when drug efficacy is less than 100%. We derive sufficient conditions for the global asymptotic stability of the uninfected steady state. We show that the time delay has no effect on the local asymptotic stability of the uninfected steady state, but can destabilize the infected steady state, leading to a Hopf bifurcation to periodic solutions in the realistic parameter ranges.
MSC:
92C50Medical applications of mathematical biology
34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models
92C60Medical epidemiology
34K18Bifurcation theory of functional differential equations
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