一类具有免疫反应的时滞病毒模型的稳定性

The Stability of a Delay Virus Model With Immune Response

建立具有免疫反应的时滞HIV动力学模型,引入以表示机体免疫系统从接受抗原刺激到产生新的毒性T淋巴细胞(CTL)所产生的时间为时滞参数。讨论系统解的非负性和有界性,得到确定模型动力学性态的基本再生数。通过构造适当的Lyapunov函数,应用LaSalle不变原理,证明了当基本再生数小于1时,无病平衡点全局渐近稳定,此时HIV在个体体内最终灭绝。最后利用Matlab软件进行数值模拟,验证了理论结果的合理性。

In this paper,we built a delay HIV dynamics model with immune response, which incorporates the duration for the the body＇s immune system from receiving antigen stimulation to produce new eytotoxic lymphocyte （CTL） as the delay parameter. Then discussed the nonnegativity and boundedness of the solution. The basic reproduction number is obtained,which determines the dynamical behaviors of the infection model. By constructing suitable Lyapunov functions and applying LaSalle＇s invariance principle we have proven that when the basic reproduction number is less than 1 ,the infection -free equilibrium is globally asymptotically stable, which implies that HIV dies out in - host eventually. At last the numerical simulation is given with the Matlab software, and the rationality of the theoretical result is verified.