具有两类靶细胞和潜伏感染的HIV感染模型
A Model of HIV Infection with Two Types of Target Cells and Latent Infection
摘要: 本文研究具有潜伏感染阶段的HIV在两种不同类型靶细胞(活化的CD4+T细胞和巨噬细胞)中的传播动力学，考虑HIV感染的多个方面，包括病毒复制、细胞感染、药物治疗干预，以及潜伏感染细胞的作用，建立具有两类靶细胞的数学模型。该模型存在无病平衡点和感染平衡点，通过对模型特征方程根的分析得到各平衡点的局部渐近稳定性。我们关注抗逆转录病毒药物(RTIs和PIs)对HIV传播的抑制效果，并探讨这些药物在不同靶细胞中的作用。数值模拟结果表明，模型的动态行为受到药物抑制效果以及其它关键生物参数的显著影响。特别是，我们展示在特定的药物效能和病毒感染参数下，系统能够达到无病状态或维持低病毒负荷的长期稳定状态。此外，本研究还通过数值模拟揭示不同药物组合和剂量下模型的响应，强调优化HIV治疗策略的潜在重要性。
Abstract: This paper studies the dynamics of HIV transmission in two different types of target cells (activated CD4+T cells and macrophages) with latent infection. It considers various aspects of HIV infection, including viral replication, cell infection, antiretroviral intervention, and the role of latently infected cells, establishing a mathematical model with two types of target cells. The model exhibits both disease-free and infected equilibrium points, and the local asymptotic stability of each equilibrium point is determined by analyzing the roots of the model’s characteristic equation. We focus on the inhibitory effects of antiretroviral drugs (RTIs and PIs) on HIV transmission and explore the effects of these drugs in different target cells. Numerical simulations indicate that the model’s dynamics are significantly influenced by the drug inhibition efficacy and other key biological parameters. In particular, we demonstrate that under certain drug efficacy and viral infection parameters, the system can achieve a disease-free state or maintain a long-term stable state with a low viral load. Moreover, this study reveals the model's response under different drug combinations and dosages through numerical simulations, emphasizing the potential importance of optimizing HIV treatment strategies.
文章引用：张佳豪, 郭黄涛, 王艳. 具有两类靶细胞和潜伏感染的HIV感染模型[J]. 应用数学进展, 2024, 13(6): 2687-2700. https://doi.org/10.12677/aam.2024.136257

参考文献

[1] Clark, I.C., Wheeler, M.A., Lee, H.-G., Li, Z., Sanmarco, L.M., Thaploo, S., et al. (2023) Identification of Astrocyte Regulators by Nucleic Acid Cytometry. Nature, 614, 326-333. [Google Scholar] [CrossRef] [PubMed]
[2] Bacchus-Souffan, C., Fitch, M., Symons, J., Abdel-Mohsen, M., Reeves, D.B., Hoh, R., et al. (2021) Relationship between CD4 T Cell Turnover, Cellular Differentiation and HIV Persistence during Art. PLOS Pathogens, 17, e1009214. [Google Scholar] [CrossRef] [PubMed]
[3] Perelson, A.S., Essunger, P., Cao, Y., Vesanen, M., Hurley, A., Saksela, K., et al. (1997) Decay Characteristics of HIV-1-Infected Compartments during Combination Therapy. Nature, 387, 188-191. [Google Scholar] [CrossRef] [PubMed]
[4] Pankavich, S. (2015) The Effects of Latent Infection on the Dynamics of HIV. Differential Equations and Dynamical Systems, 24, 281-303. [Google Scholar] [CrossRef] 
[5] Shen, L., Peterson, S., Sedaghat, A.R., McMahon, M.A., Callender, M., Zhang, H., et al. (2008) Dose-Response Curve Slope Sets Class-Specific Limits on Inhibitory Potential of Anti-HIV Drugs. Nature Medicine, 14, 762-766. [Google Scholar] [CrossRef] [PubMed]
[6] Wang, X., Song, X., Tang, S. and Rong, L. (2016) Dynamics of an HIV Model with Multiple Infection Stages and Treatment with Different Drug Classes. Bulletin of Mathematical Biology, 78, 322-349. [Google Scholar] [CrossRef] [PubMed]
[7] Edwards, C.H. and Penney, D.E. (2015) Differential Equations with Boundary-Value Problems. 5th Edition, Machinery Industry Press.
[8] Li, F. and Ma, W. (2018) Dynamics Analysis of an HTLV-1 Infection Model with Mitotic Division of Actively Infected Cells and Delayed CTL Immune Response. Mathematical Methods in the Applied Sciences, 41, 3000-3017. [Google Scholar] [CrossRef] 
[9] Perelson, A.S., Kirschner, D.E. and De Boer, R. (1993) Dynamics of HIV Infection of CD4+ T Cells. Mathematical Biosciences, 114, 81-125. [Google Scholar] [CrossRef] [PubMed]
[10] Elaiw, A.M. and AlShamrani, N.H. (2020) HTLV/HIV Dual Infection: Modeling and Analysis. Mathematics, 9, Article 51. [Google Scholar] [CrossRef] 
[11] Adams, B.M., Banks, H.T., Kwon, H.-D. and Tran, H.T. (2004) Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches. Mathematical Biosciences and Engineering, 1, 223-241. [Google Scholar] [CrossRef] [PubMed]
[12] Adams, B.M., Banks, H.T., Davidian, M., Kwon, H., Tran, H.T., Wynne, S.N., et al. (2005) HIV Dynamics: Modeling, Data Analysis, and Optimal Treatment Protocols. Journal of Computational and Applied Mathematics, 184, 10-49. [Google Scholar] [CrossRef] 
[13] Callaway, D.S. and Perelson, A.S. (2002) HIV-1 Infection and Low Steady State Viral Loads. Bulletin of Mathematical Biology, 64, 29-64. [Google Scholar] [CrossRef] [PubMed]
[14] Mohri, H., Bonhoeffer, S., Monard, S., Perelson, A.S. and Ho, D.D. (1998) Rapid Turnover of T Lymphocytes in SIV-Infected Rhesus Macaques. Science, 279, 1223-1227. [Google Scholar] [CrossRef] [PubMed]
[15] Wang, Y., Zhou, Y., Brauer, F. and Heffernan, J.M. (2012) Viral Dynamics Model with CTL Immune Response Incorporating Antiretroviral Therapy. Journal of Mathematical Biology, 67, 901-934. [Google Scholar] [CrossRef] [PubMed]
[16] Hill, A.L., Rosenbloom, D.I.S., Nowak, M.A. and Siliciano, R.F. (2018) Insight into Treatment of HIV Infection from Viral Dynamics Models. Immunological Reviews, 285, 9-25. [Google Scholar] [CrossRef] [PubMed]
[17] Tuckwell, H.C. and Le Corfec, E. (1998) A Stochastic Model for Early HIV-1 Population Dynamics. Journal of Theoretical Biology, 195, 451-463. [Google Scholar] [CrossRef] [PubMed]
[18] Wang, Y., Liu, J. and Liu, L. (2016) Viral Dynamics of an HIV Model with Latent Infection Incorporating Antiretroviral Therapy. Advances in Difference Equations, 2016, Article No. 225. [Google Scholar] [CrossRef] 
[19] Elaiw, A.M., Raezah, A.A. and Azoz, S.A. (2018) Stability of Delayed HIV Dynamics Models with Two Latent Reservoirs and Immune Impairment. Advances in Difference Equations, 2018, Article No. 414. [Google Scholar] [CrossRef] 
[20] Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M. and Ho, D.D. (1996) HIV-1 Dynamics in vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time. Science, 271, 1582-1586. [Google Scholar] [CrossRef] [PubMed]
[21] Nelson, P.W., Murray, J.D. and Perelson, A.S. (2000) A Model of HIV-1 Pathogenesis that Includes an Intracellular Delay. Mathematical Biosciences, 163, 201-215. [Google Scholar] [CrossRef] [PubMed]
[22] Perelson, A.S. and Nelson, P.W. (1999) Mathematical Analysis of HIV-1 Dynamics in Vivo. SIAM Review, 41, 3-44. [Google Scholar] [CrossRef] 
[23] Wang, X., Ge, Q. and Chen, Y. (2020) Threshold Dynamics of an HIV Infection Model with Two Distinct Cell Subsets. Applied Mathematics Letters, 103, Article 106242. [Google Scholar] [CrossRef] 

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