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.
Original language | English |
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Pages (from-to) | 709-720 |
Number of pages | 12 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 385 |
Issue number | 2 |
DOIs | |
State | Published - 15 Jan 2012 |
Externally published | Yes |
Keywords
- Compound matrices
- Global stability
- HIV
- Lyapunov functions