年龄结构CD4^+T-细胞模型复杂动力学分析

COMPLEX DYNAMICS OF A CD4^+ T-CELL MODEL WITH AGE STRUCTURE

研究了一类年龄结构的CD4^+T-细胞模型.得到了控制HIV病毒扩散的阈值R_0.当R_0<1时,无病平衡点全局渐近稳定,病毒在人体内消除;当R_0>1,且-r+(2αrT~*)/(T_(max))>0,地方病平衡点局部渐近稳定,病毒在人体内繁殖;当R_0>1,且-r+(2αrT~*)/(T_(max))<0,系统由感染年龄而产生的复杂动力学行为,如Hopf分支,四周期解及混沌等.最后对模型的复杂动力学行为进行了数值模拟.

A class of CD4^＋ T-cell model with age structure is investigated.Disperse threshold for the control of the HIV virus R0 is obtained.If Rq 1,the disease-free equilibrium is globally asymptotically stable,the HIV virus in the body dies out;If Ro 1 and -r＋2αrT^＊/Tmax〉0,the endemic equilibrium is locally asymptotically stable,the HIV virus spreads in the body;If R0 1 and -r＋2αrT^＊/Tmax〉0,complex dynamics induced by the age structure are investigated by the global Hopf bifurcation theorem.Finally the complex dynamics is illustrated by the simulations.