一类带有治愈率的HIV感染CD4^+T细胞的分数阶微分方程模型

A Fractional Differential Equation Model of HIV Infection of CD4^+T-cells with Cure Rate

提出分数阶的HIV-免疫系统,在一类带有饱和HIV感染的CD4+T细胞常微分方程模型的基础上引入一个带有治愈率的HIV感染CD4+T细胞分数阶微分方程模型.通过分析,得到了该模型正解的全局存在唯一性条件及模型平衡点局部渐近稳定的充分条件.最后用Matlab对模型平衡点的稳定性进行了数值模拟.

A fractional-order HIV-immune system was proposed, a fractional differential equation model of HIV infection of CD4＋ T-cells with cure rate was established on the base of HIV infection of CD4＋ T-cells ordinary differential equation model with saturation response of the infection rate. By analysis, conditions for which a positive solution of the system exists in the global spaces and sufficient conditions on the parameters for the local asymptotic stability of systems equilibrium point was obtained. Finally, numerical simulations were presented to illustrate the stability of equilibrium point by Matlab.