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

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1836-1848.

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

徐瑞*(),杨琰

^{山西大学复杂系统研究所, 太原 030006}

收稿日期:2021-09-29 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 徐瑞 E-mail:rxu88@163.com
基金资助:
国家自然科学基金(11871316)

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

Rui Xu*(),Yan Yang

^{Complex Systems Research Center, Shanxi University, Taiyuan 030006}

Received:2021-09-29 Online:2022-12-26 Published:2022-12-16
Contact: Rui Xu E-mail:rxu88@163.com
Supported by:
the NSFC(11871316)

摘要/Abstract

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.

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

Abstract:

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.

Key words: HTLV-I infection, Immune delay, Saturated CTL immune response, Immune impairment, Hopf bifurcation

中图分类号:

O175.1

徐瑞,杨琰. 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[J]. 数学物理学报, 2022, 42(6): 1836-1848.

Rui Xu,Yan Yang. Dynamics of an HTLV-I Infection Model with Delayed and Saturated CTL Immune Response and Immune Impairment[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1836-1848.

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