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

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.

图/表 3

参考文献 21

1	Cann A J, Chen Isy. Human T-cell Leukemia virus type I and II//Fields B N, Knipe D M, Howley P M. Field Virology. Philadelphia: Lippincott-Raven Publishers, 1996: 1849-1880
2	Bangham C R M . The immune response to HTLV-I. Curr Opin Immunol, 2000, 12, 397- 402 doi: 10.1016/S0952-7915(00)00107-2
3	Jacobson S . Immunopathogenesis of human T cell lymphotropic virus type I-associated neurologic disease. J Infect Dis, 2002, 186, S187- S192 doi: 10.1086/344269
4	Asquith B , Bangham C R M . Quantifying HTLV-I dynamics. Immunol Cell Biol, 2007, 85, 280- 286 doi: 10.1038/sj.icb.7100050
5	Beretta E , Kuang Y . Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J Math Anal, 2002, 33, 1144- 1165 doi: 10.1137/S0036141000376086
6	Asquith B , Bangham C R M . How does HTLV-I persist despite a strong cell-mediated immune response?. Trends Immunol, 2008, 29, 4- 11 doi: 10.1016/j.it.2007.09.006
7	Khajanchi S , Bera S , Roy T K . Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes. Math Comput Simul, 2021, 180, 354- 378 doi: 10.1016/j.matcom.2020.09.009
8	Tian X , Xu R . Global stability and hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response. Appl Math Comput, 2014, 237, 146- 154
9	Li M Y , Shu H . Multiple stable periodic oscillations in a mathematical model of CTL response to HTLV-I infection. Bull Math Biol, 2011, 73, 1774- 1793 doi: 10.1007/s11538-010-9591-7
10	Gómez-Acevedo H , Li M Y , Jacobson S . Multistability in a model for CTL response to HTLV-I infection and its implications to HAM/TSP development and prevention. Bull Math Biol, 2010, 72, 681- 696 doi: 10.1007/s11538-009-9465-z
11	Wang A , Li M Y . Viral dynamics of HIV-1 with CTL immune response. Discrete Contin Dyn Syst-Ser B, 2021, 26, 2257- 2272 doi: 10.3934/dcdsb.2020212
12	Wang S , Song X , Ge Z . Dynamics analysis of a delayed viral infection model with immune impairment. Appl Math Model, 2011, 35, 4877- 4886 doi: 10.1016/j.apm.2011.03.043
13	Rosenberg E S , Altfeld M , Poon S H , et al. Immune control of HIV-1 after early treatment of acute infection. Nature, 2000, 407, 523- 526 doi: 10.1038/35035103
14	Regoes R R , Wodarz D , Nowak M A . Virus dynamics: the effect of target cell limitation and immune responses on virus evolution. J Theor Biol, 1998, 191, 451- 462 doi: 10.1006/jtbi.1997.0617
15	Hale J K, Verduyn Lunel S M. Introduction to Functional Differential Equations. New York: Springer, 1993
16	van den Driessche P , Watmough J . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci, 2002, 180 (1/2): 29- 48
17	Yan X, Li W. Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays. Discrete Dyn Nat Soc, 2006, 2006: Article ID 032529
18	Song Y , Yuan S . Bifurcation analysis in a predator-prey system with time delay. Nonlinear Anal: Real World Appl, 2006, 7, 265- 284 doi: 10.1016/j.nonrwa.2005.03.002
19	Wu J . Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc, 1998, 350, 4799- 4838 doi: 10.1090/S0002-9947-98-02083-2
20	Song C , Xu R . Mathematical analysis of an HTLV-I infection model with the mitosis of CD4⁺ T cells and delayed CTL immune response. Nonlinear Anal-Model Control, 2021, 26, 1- 20 doi: 10.15388/namc.2021.26.21050
21	Martcheva M. An Introduction to Mathematical Epidemiology. New York: Springer, 2015

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[12]	吴云华, 袁晓凤, 刘世泽. 一类三维生态动力系统的Hopf分支[J]. 数学物理学报, 1998, 18(1): 70-77.