一类具有胞内时滞和饱和CTL免疫反应的HTLV-I感染模型的全局动力学性态  

Global dynamics of a type of HTLV-I infection model with intracellular delay and saturated CTL immune response

作　　者：张丽茹 徐瑞 ZHANG Li-ru;XU Rui(Complex Systems Research Center,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学复杂系统研究所,山西太原030006

出　　处：《高校应用数学学报（A辑）》2021年第3期300-308,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11871316,11801340);山西省自然科学基金(201801D121006,201801D221007)。

摘　　要：研究了一类具有胞内时滞,饱和感染率及饱和CTL免疫反应的HTLV-I感染动力学模型.通过计算得到了模型的两个阙值条件:病毒感染再生数和免疫反应再生数,分析了可行平衡点的存在性;通过分析特征方程根的分布讨论了可行平衡点的局部渐近稳定性;通过构造适当的Lyapunov泛函并结合LaSalle不变性原理得出:若病毒感染再生数小于1,则病毒未感染平衡点是全局渐近稳定的,病毒被清除;若免疫反应再生数小于1且病毒感染再生数大于1,则免疫未激活感染平衡点是全局渐近稳定的;若免疫反应再生数大于1,则免疫激活感染平衡点是全局渐近稳定的.最后通过对病毒感染再生数和免疫反应再生数进行敏感性分析,讨论了参数和再生数之间的相关性.This paper studies an HTLV-I infection model with intracellular delay,saturated infection rate and saturated CTL immune response.By calculation,two threshold conditions of the model:virus infection reproduction number and immune response reproduction number are derived.The existence of feasible equilibria is analyzed.The local asymptotic stability each of the feasible equilibria is discussed by analyzing the distribution of roots of characteristic equations.By constructing suitable Lyapunov functionals and combining with LaSalle's invariance principle,it is proved that if the virus infection reproduction number is less than 1,the virus infection-free equilibrium is globally asymptotically stable,and the virus is eliminated;if the immune response reproduction number is less than 1 and the virus infection reproduction number is greater than 1,then the CTL-inactivated infection equilibrium is globally asymptotically stable;if the immune response reproduction number is greater than 1,the CTL-activated infection equilibrium is globally asymptotically stable.Finally,through sensitivity analysis of virus infection reproduction number and immune response reproduction number,the correlations between parameters and reproduction numbers are discussed.

关 键 词：HTLV-I感染 胞内时滞 CTL免疫反应 稳定性 LYAPUNOV泛函 LaSalle不变性原理 

分 类 号：O175.13[理学—数学]