TY - JOUR
T1 - Global stability for an HIV-1 infection model including an eclipse stage of infected cells
AU - Buonomo, Bruno
AU - Vargas-De-León, Cruz
PY - 2012/1/15
Y1 - 2012/1/15
N2 - 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.
AB - 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.
KW - Compound matrices
KW - Global stability
KW - HIV
KW - Lyapunov functions
UR - http://www.scopus.com/inward/record.url?scp=80052153949&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2011.07.006
DO - 10.1016/j.jmaa.2011.07.006
M3 - Artículo
SN - 0022-247X
VL - 385
SP - 709
EP - 720
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -