具有非局部感染和周期治疗的HIV感染模型的时空动力学分析

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 209-226.

具有非局部感染和周期治疗的HIV感染模型的时空动力学分析

吴鹏^1,^2,^*(),何泽荣³

1.杭州电子科技大学理学院杭州 310018
2.浙江财经大学数据科学学院杭州 310018
3.杭州电子科技大学运筹与控制研究所杭州 310018

收稿日期:2022-11-07 修回日期:2023-10-07 出版日期:2024-02-26 发布日期:2024-01-10
通讯作者: 吴鹏, E-mail:hzpengwu@163.com
基金资助:
国家自然科学基金(12201557);国家自然科学基金(12201007);国家自然科学基金(11871185);浙江省教育厅一般项目(Y202249921);安徽省自然科学基金(2108085MA10)

Spatio-temporal Dynamics of HIV Infection Model with Periodic Antiviral Therapy and Nonlocal Infection

Wu Peng^1,^2,^*(),He Zerong³

1. School of Sciences, Hangzhou Dianzi University, Hangzhou 310018
2. School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018
3. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018

Received:2022-11-07 Revised:2023-10-07 Online:2024-02-26 Published:2024-01-10
Supported by:
NSFC(12201557);NSFC(12201007);NSFC(11871185);Foundation of Zhejiang Provincial Education Department(Y202249921);Anhui Provincial Natural Science Foundation(2108085MA10)

摘要/Abstract

摘要：

该文建立了一类非自治反应扩散 HIV 细胞模型来研究周期治疗、非局部感染对 HIV 感染时空动力学的影响. 具体地, 首先推导出模型基本再生数$\mathcal{R}_0$, 其由下一代再生算子$\mathcal{R}$的谱半径所定义. 然后对模型的动力学行为进行分析, 其中包括无感染平衡态的全局稳定性、HIV 感染的一致持久性以及周期正平衡态的存在性. 最后, 通过数值模拟验证了理论结果的正确性并分析了相关重要因素对 HIV 感染进程的影响, 为 HIV 的临床治疗提供有价值的参考建议.

关键词: HIV, 反应扩散模型, 空间异质, 非局部感染, 周期抗病毒治疗, 阈值动力学

Abstract:

In this paper, a non-autonomous reaction-diffusion HIV cell model is established to study the effects of periodic antiviral therapy, non local infection and spatial heterogeneity on HIV infection spatio-temporal dynamics. Specifically, we derive the functional expression of the basic regeneration number of the model$\mathcal{R}_0$, which is defined by the spectral radius of the next generation regeneration operator$\mathcal{R}$. Then the dynamical behaviors of the model is analyzed, including the global stability of the HIV infection-free steady state, the uniform persistence of HIV infection and the existence of periodic positive steady state. Finally, we conduct some numerical simulations to verify the theoretical results, and study the influence of relevant important factors on the process of HIV infection. Our works can provide some valuable reference suggestions for the clinical treatment of HIV infection.

Key words: HIV, Reaction-diffusion model, Spatial heterogeneity, Nonlocal infection, Periodic antiviral therapy, Threshold dynamics

中图分类号:

O175.23

吴鹏, 何泽荣. 具有非局部感染和周期治疗的HIV感染模型的时空动力学分析[J]. 数学物理学报, 2024, 44(1): 209-226.

Wu Peng, He Zerong. Spatio-temporal Dynamics of HIV Infection Model with Periodic Antiviral Therapy and Nonlocal Infection[J]. Acta mathematica scientia,Series A, 2024, 44(1): 209-226.

图/表 6

图1

图2

图3

图4

图5

图6

参考文献 31

[1]	Vaidya N K, Rong L. Modeling pharmacodynamics on HIV latent infection: Choice of drugs is key to successful cure via early therapy. SIAM J Appl Math, 2017, 77: 1781-1804 doi: 10.1137/16M1092003
[2]	Wu P, Zhao H. Dynamics of an HIV infection model with two infection routes and evolutionary competition between two viral strains. Appl Math Model, 2020, 84: 240-264 doi: 10.1016/j.apm.2020.03.040
[3]	Rong L, Feng Z, Perelson A S. Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy. SIAM J Appl Math, 2007, 67: 731-756 doi: 10.1137/060663945
[4]	Wang X, Song X, Tang S, Rong L. Dynamics of an HIV model with multiple infection stages and treatment with different drugs classes. Bull Math Biol, 2016, 78: 322-349 doi: 10.1007/s11538-016-0145-5
[5]	邓萌, 徐瑞. 一类具有 CTL 免疫反应和免疫损害的 HIV 感染动力学模型的稳定性分析. 数学物理学报, 2022, 42A(5): 1592-1600
	Deng M, Xu R. MenStability analysis of an HIV infection dynamic model wit CTL immune response and immune impairment. Acta Math Sci, 2022, 42A(5): 1592-1600
[6]	娄洁, 马之恩, 邵一鸣. HIV-1 的表型间变异与免疫因子相互作用的动力学模型. 数学物理学报, 2007, 27A(5): 898-906
	Lou J, Ma Z, Shao M. Modelling the interactions between the HIV-1 phenotypes and the cytokines. Acta Math Sci, 2007, 42A(5): 1592-1600
[7]	Ren X, Tian Y, Liu L, Liu X. A reaction-diffusion within-host HIV model with cell-to-cell transmission. J Math Biol, 2018, 76: 1831-1872 doi: 10.1007/s00285-017-1202-x pmid: 29305736
[8]	Wu P, Zhao H. Dynamical analysis of a nonlocal delayed and diffusive HIV latent infection model with spatial heterogeneity. J Franklin Institute, 2021, 358: 5552-5587 doi: 10.1016/j.jfranklin.2021.05.014
[9]	吴鹏, 赵洪涌. 基于空间异质反应扩散 HIV 感染模型的最优治疗策略. 应用数学学报, 2022, 45(5): 752-766
	Wu P, Zhao H. Optimal treatment strategies for a reaction-dffusion HIV infection model with spatial heterogeneity. Acta Math Appl Sinica, 2022, 45(5): 752-766
[10]	王良平. 强一致收敛下的初值敏感性与等度连续性. 浙江大学学报(理学版), 2012, 39(3): 270-272
	Wang L. The snsitive dependence on initial conditions and the equicontinuit under strongly uniform convergence. J Zhejiang Univ (Scicence Edition), 2012, 39(3): 270-272
[11]	Wang W, Wang X, Feng Z. Time periodic reaction-diffusion equations for modeling 2-LTR dynamics in HIV-infected patients. Nonlinear Anal RWA, 2021, 57: 103184
[12]	Wu P, Zheng S, He Z. Evolution dynamics of a time-delayed reaction-diffusion HIV latent infection model with two strains and periodic therapies. Nonlinear Anal RWA, 2022, 67: 103559
[13]	World Health Organization, 10 facts about HIV/AIDS fact sheet No. 204 updated July 2018. Available from: http://www.who.int/news-room/facts-in-pictures/detail/hiv-aids . [2022-11-01]
[14]	Fang H, Stone E, Piacenti F. Tenofovir disoproxil fumarate: A nucleotide reverse transcriptase inhibitor for the treatment of HIV infection. Clin Ther, 2002, 24: 1515-1548 pmid: 12462284
[15]	Shirakawa K, Chavez L, Hakre S, et al. Reactivation of latent HIV by histone deacetylase inhibitors. Trends Microbio, 2013, 21(6): 277-285
[16]	Rasmussen T, Schmeltz S, Brinkmann C, et al. Comparison of HDAC inhibitors in clinical development: Effect on HIV production in latently infected cells and T-cell activation. Hum Vaccin Immunother, 2013, 9(5): 993-1001 doi: 10.4161/hv.23800
[17]	谢强军, 张光新, 周泽魁. 一类周期反应扩散方程正周期解的存在性. 数学物理学报, 2009, 29A(2): 465-474
	Xie Q J, Zhang G X, Zhou Z K. The existece of positive periodic solutions for a kind of periodic reaction-diffusion equations. Acta Math Sci, 2009, 29A(2): 465-474
[18]	Levy J A. HIV and the Pathogenesis of AIDS. Washington, DC: ASM Press, 2007
[19]	De Mottoni P, Orlandi E, Tesei A. Asymptotic behavior for a system describing epidemics with migration and spatial spread of infection. Nonlinear Anal, 1979, 3(5): 663-675 doi: 10.1016/0362-546X(79)90095-6
[20]	Pazy A. Semigroups of Linear Operators and Application to Partial Differential Equations. New York: Springer-Verlag, 1983
[21]	Yang J, Xu R, Sun H. Dynamics of a seasonal brucellosis diseaase model with nonlocal transmission and spatial diffusion. Commun Nonlinear Sci Numeri Simult, 2021, 94: 105551
[22]	Martin R H, Smith H L. Abstract functional dierential equations and reaction-diffusion systems. Trans Amer Math Soc, 1990, 321: 1-44
[23]	Zhang L, Wang Z C, Zhao X Q. Threshold dynamics of a time periodic reaction-diffusion epidemic model with latent period. J Differ Equat, 2015, 258: 3011-3036 doi: 10.1016/j.jde.2014.12.032
[24]	《数学辞海》总编辑委员会. 《数学辞海》第3卷. 南京: 东南大学出版社, 2002
	Mathematical Dictionary Editoral Committe. Mathematical Dictionary Volume iii. Nanjing: Southeast University Press, 2002
[25]	Krein M G, Rutman M A. Linear operators leaving invariant a cone in a Banach space. Uspehi Matem Nauk (NS), 1948, 23: 3-95
[26]	Liu Z Z, When S Z, Wang H, Jin Z. Analysis of a local diffusive model with seasonality and nonlocal incidence of infection. SIAM J Appl Math, 2019, 79: 2218-2241 doi: 10.1137/18M1231493
[27]	Peng R, Zhao X Q. A reaction-diffusion SIS epidemic model in a time-periodic environment. Nonlinearity, 2012, 25: 1451-1471 doi: 10.1088/0951-7715/25/5/1451
[28]	Zhao X Q. Uniform persistence and periodic coexistence states in infnite-dimension periodic semiflows with applications. Canad Appl Math Quart, 1995, 3: 473-495
[29]	Magal P, Zhao X Q. Global attractors and steady states for uniformly persistent dynamical systems. SIAM J Math Anal, 2005, 37: 251-275 doi: 10.1137/S0036141003439173
[30]	Zhao X Q. Dynamical Systems in Population Biology. Switzerland: Springer, 2003
[31]	Wu P, Wang X, Wang H. Threshold dynamics of nonlocal dispersal HIV/AIDS epidemic model with spatial heterogeneity and antiretroviral therapy. Commun Nonlinear Sci Numer Simulat, 2022, 115: 106728 doi: 10.1016/j.cnsns.2022.106728