一类具有CTL作用的HIV感染模型的全局稳定性

Global Stability of an HIV Infection Model with CTL Effect

通过假设无HIV感染时个体体内的CTL细胞存在常数输入和被感染CD4+T细胞对CTL细胞繁殖的影响具有饱和形式,本文建立了一类具有CTL作用的HIV感染模型,得到了确定模型动力学性态的基本再生数.当基本再生数不大于1时,健康平衡点在可行域上是全局渐近稳定的,即HIV在个体体内最终灭绝;当基本再生数大于1时,模型的惟一感染平衡点在可行域内是全局渐近稳定的,即HIV将在个体体内持续存在,并且其浓度最终趋于一个正常数.

An HIV infection model with CTL effect is established by assuming that there is a constant input of CTL cells in the absence of HIV infection,and that the impact of the infected CD4＋T cells on the proliferation of CTL cells is with a form of saturation.The basic reproduction number is obtained,which determines the dynamical behaviors of the model.When the number is not greater than 1,the healthy equilibrium is globally stable on the feasible region,which implies that HIV dies out in-host eventually;when the number is greater than 1,the model has a unique infection equilibrium,which is globally stable in the feasible region,that is,HIV persists in body of the infected individuals,and the concentration of HIV approaches a positive number in-host.