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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 1298.92053)]. 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.

##### MSC:
 92C50 Medical applications (general) 34D23 Global stability of solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 65C20 Probabilistic models, generic numerical methods in probability and statistics
##### Keywords:
HIV; Lyapunov functions; compound matrices; global stability
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##### References:
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