非线性感染率的HIV模型的动力学研究

Study of HIV Model with Nonlinear Infection Rate

众所周知,数学模型为引起人类免疫力缺乏的HIV-1型病毒和引起肝炎的HCV病毒的研究提供了重要信息.然而几乎所有的数学模型感染率都是线性的,而线性只是反映了T细胞与病毒分子之间的简单作用.这篇论文研究了一类具有非线性传染率的数学模型.通过分析我们得到了无病平衡态P0全局渐近稳定的条件及染病平衡态P-的稳定性条件.

It is well known that the mathematical models provide very significant informations for the research of human immunodeficiency virus-type 1 （HIV-1） and hepatitis C virus （HCV）. However, the infection rate of almost all mathematical models is linear, the linearity shows the simple interaction between the T cells and the viral particles. This paper considers the mathematical model with one class of the non-linear infection rate. We analyzed that the sufficient conditions for the global stability of the uninfected equilibrium state P0 and the infected equilibrium state P^-.