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. 2011 Jul 12;385(2):709–720. doi: 10.1016/j.jmaa.2011.07.006

Global stability for an HIV-1 infection model including an eclipse stage of infected cells

Bruno Buonomo a, Cruz Vargas-De-León b,c,⁎
PMCID: PMC7127580  PMID: 32287385

Abstract

We consider the mathematical model for the viral dynamics of HIV-1 introduced in Rong et al. (2007) [37]. 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. In Rong et al. (2007) [37], the stability of the infected equilibrium has been analyzed locally. Here, we perform the global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on the higher-order generalization of Bendixsonʼs criterion. We obtain sufficient conditions written in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.

Keywords: HIV, Lyapunov functions, Compound matrices, Global stability

Submitted by J. Shi

Contributor Information

Bruno Buonomo, Email: buonomo@unina.it.

Cruz Vargas-De-León, Email: leoncruz82@yahoo.com.mx.

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