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

Bruno Buonomo; Cruz Vargas-De-León

doi:10.1016/j.jmaa.2011.07.006

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

J Math Anal Appl. 2012 Jan 15;385(2):709-720. doi: 10.1016/j.jmaa.2011.07.006. Epub 2011 Jul 12.

Authors

Bruno Buonomo¹, Cruz Vargas-De-León^{2

3}

Affiliations

¹ Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy.
² Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas C.U., Chilpancingo, Guerrero, Mexico.
³ Facultad de Estudios Superiores Zaragoza, UNAM, Col. Ejército de Oriente, Iztapalapa, Mexico.

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 Bendixson's 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: Compound matrices; Global stability; HIV; Lyapunov functions.