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Global stability for an HIV-1 infection model including an eclipse stage of infected cells. (English) Zbl 1223.92024
Summary: We consider the mathematical model for the viral dynamics of HIV-1 introduced by L. Rong et al. [J. Theor. Biol. 247, 804–818 (2007); see also Bull. Math. Biol. 69, No. 6, 2027–2060 (2007; Zbl 05265722)]. One main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class. The viral dynamics is described by four nonlinear ordinary differential equations. Rong et al. have analyzed the stability of the infected equilibrium locally. We perform a global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on a higher-order generalization of Bendixson’s criterion. We obtain sufficient conditions in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.
92C50Medical applications of mathematical biology
34D23Global stability of ODE
34C60Qualitative investigation and simulation of models (ODE)
65C20Models (numerical methods)
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