具有免疫时滞、饱和CTL免疫反应和免疫损害的HTLV-I感染模型的动力学性态  

Dynamics of an HTLV-I Infection Model with Delayed and Saturated CTL Immune Response and Immune Impairment

作　　者：徐瑞 杨琰 Xu Rui;Yang Yan(Complex Systems Research Center,Shanxi University,Taiyuan 030006)

机构地区：[1]山西大学复杂系统研究所,太原030006

出　　处：《数学物理学报（A辑）》2022年第6期1836-1848,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871316)。

摘　　要：该文研究一类具有免疫时滞、饱和CTL免疫反应和免疫损害的HTLV-I感染动力学模型.通过计算得到了免疫未激活再生率和免疫激活再生率.通过构造适当的Lyapunov泛函,并利用LaSalle不变性原理,证明了当免疫未激活再生率小于1时,病毒未感染平衡点是全局渐近稳定的;当免疫激活再生率小于1且免疫未激活再生率大于1时,免疫未激活平衡点是全局渐近稳定的;在免疫时滞为0的情形下,当免疫激活再生率大于1时,免疫激活平衡点是全局渐近稳定的.当免疫时滞大于某一临界值时,给出了免疫激活平衡点处产生Hopf分支的条件.最后,通过数值模拟对理论结果进行了说明.In this paper,an HTLV-I infection model with delayed and saturated CTL immune response and immune impairment is developed.By calculations,the existences of feasible equilibria are established,immunity-inactivated and immunity-activated reproduction ratios are also derived.Under the assistance of proper Lyapunov functionals and LaSalle's invariance principle,it is shown that the infection-free equilibrium is globally asymptotically stable if the immunity-inactivated reproduction ratio is less than unity;the immunity-inactivated equilibrium is globally asymptotically stable if the immunity-activated reproduction ratio is less than unity,while the immunity-inactivated reproduction ratio is greater than unity;the immunity-activated equilibrium is globally asymptotically stable(when the time delay equals to zero)if the immunity-activated reproduction ratio is greater than unity.A Hopf bifurcation at the immunity-activated equilibrium occurs as the time delay crosses a critical value.Finally,numerical simulations are performed to illustrate the theoretical results.

关 键 词：HTLV-I感染 免疫时滞 饱和CTL免疫反应 免疫损害 HOPF分支 

分 类 号：O175.1[理学—数学]