Buonomo Bruno, Vargas-De-León Cruz
Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy.
Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas C.U., Chilpancingo, Guerrero, Mexico.
J Math Anal Appl. 2012 Jan 15;385(2):709-720. doi: 10.1016/j.jmaa.2011.07.006. Epub 2011 Jul 12.
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.
我们考虑Rong等人（2007年）[37]中引入的HIV-1病毒动力学数学模型。该模型的一个主要特征是包含了受感染细胞的隐蔽期，处于此阶段的细胞可能会恢复到未感染类别。病毒动力学由四个非线性常微分方程描述。在Rong等人（2007年）[37]中，已对感染平衡点的稳定性进行了局部分析。在此，我们基于Bendixson准则的高阶推广，使用两种技术——李雅普诺夫直接法和稳定性的几何方法，进行全局稳定性分析。我们得到了根据系统参数写出的充分条件。还提供了数值模拟，以更完整地呈现系统动力学。
