Stochastic dynamics and treatment strategies of an HIV infection model with quiescent cells, CTLs and antibody immune responses

Linyu Zuo; Xueyong Zhou; Xiangyun Shi; Linyu Zuo; Xueyong Zhou; Xiangyun Shi

doi:10.3934/era.2026360

Electronic Research Archive

2026, Volume 34, Issue 11: 8515-8552. doi: 10.3934/era.2026360

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Research article

Stochastic dynamics and treatment strategies of an HIV infection model with quiescent cells, CTLs and antibody immune responses

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Received: 16 July 2026 Revised: 07 September 2026 Accepted: 22 September 2026 Published: 08 October 2026

In this paper, a stochastic human immunodeficiency virus (HIV) infection model incorporating quiescent cells, cytotoxic C lymphocytes (CTLs), and antibody immune responses is formulated. First, the existence and uniqueness of the global positive solutions to the model are proven, which guarantees the well-posedness and validity of the constructed dynamic system. Second, the existence of the ergodic stationary distribution is investigated by constructing suitable stochastic Lyapunov functions. Third, the sufficient conditions for virus elimination are derived. Furthermore, optimal control strategies consistent with clinical antiviral treatment regimens are proposed to achieve a trade-off between therapeutic efficacy and economic costs. To validate the theoretical results and further compare the practical performance of different intervention schemes, numerical simulations are implemented, including theoretical verification, parameter sensitivity analysis, and comprehensive cost-effectiveness assessment of various therapeutic strategies. This study systematically clarifies the dynamical evolutionary behaviors of stochastic HIV infection and the efficacy of different control measures. The findings not only enrich the theoretical research on stochastic HIV infection model but also provide solid theoretical support and quantitative guidance for the design, assessment, and optimal selection of clinical HIV treatment strategies.
- stochastic HIV infection model,
- ergodic stationary distribution,
- virus elimination,
- optimal control strategies
Citation: Linyu Zuo, Xueyong Zhou, Xiangyun Shi. Stochastic dynamics and treatment strategies of an HIV infection model with quiescent cells, CTLs and antibody immune responses[J]. Electronic Research Archive, 2026, 34(11): 8515-8552. doi: 10.3934/era.2026360

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Abstract

In this paper, a stochastic human immunodeficiency virus (HIV) infection model incorporating quiescent cells, cytotoxic C lymphocytes (CTLs), and antibody immune responses is formulated. First, the existence and uniqueness of the global positive solutions to the model are proven, which guarantees the well-posedness and validity of the constructed dynamic system. Second, the existence of the ergodic stationary distribution is investigated by constructing suitable stochastic Lyapunov functions. Third, the sufficient conditions for virus elimination are derived. Furthermore, optimal control strategies consistent with clinical antiviral treatment regimens are proposed to achieve a trade-off between therapeutic efficacy and economic costs. To validate the theoretical results and further compare the practical performance of different intervention schemes, numerical simulations are implemented, including theoretical verification, parameter sensitivity analysis, and comprehensive cost-effectiveness assessment of various therapeutic strategies. This study systematically clarifies the dynamical evolutionary behaviors of stochastic HIV infection and the efficacy of different control measures. The findings not only enrich the theoretical research on stochastic HIV infection model but also provide solid theoretical support and quantitative guidance for the design, assessment, and optimal selection of clinical HIV treatment strategies.

References

[1]	F. Younai, Thirty years of the human immunodeficiency virus epidemic and beyond, Int. J. Oral. Sci., 5 (2013), 191–199. https://doi.org/10.1038/ijos.2013.76 doi: 10.1038/ijos.2013.76
[2]	World Health Organization, Data on the HIV Response, 2024. Available from: https://www.who.int/data/gho/data/themes/topics/topic-details/GHO/data-on-the-hiv-aids-response.
[3]	M. Tan, G. Lan, C. Wei, Dynamic analysis of HIV infection model with CTL immune response and cell-to-cell transmission, Appl. Math. Lett., 156 (2024), 109140. https://doi.org/10.1016/j.aml.2024.109140 doi: 10.1016/j.aml.2024.109140
[4]	J. Danane, K. Allali, Optimal control of an HIV model with CTL cells and latently infected cells, Numer. Algebra Control Optimi., 10 (2020), 207–225. https://doi.org/10.3934/naco.2019048 doi: 10.3934/naco.2019048
[5]	A. Wang, M. Y. Li, Viral dynamics of HIV-1 with CTL immune response, Discrete. Cont. Dyn. B, 26 (2021), 2257–2272. https://doi.org/10.3934/dcdsb.2020212 doi: 10.3934/dcdsb.2020212
[6]	T. Guo, H. Liu, C. Xu, F. Yan, Dynamics of a delayed HIV-1 infection model with saturation incidence rate and CTL immune response, Int. J. Bifurcation Chaos, 26 (2016), 1650234. https://doi.org/10.1142/S0218127416502345 doi: 10.1142/S0218127416502345
[7]	Z. Ye, Y. Zhou, Z. Zheng, C. Chen, Stability and Hopf bifurcation of a cytokine-enhanced HIV infection model with antibody immune response delay, Int. J. Biomath., 18 (2025), 2450037. https://doi.org/10.1142/s0218127424501335 doi: 10.1142/s0218127424501335
[8]	D. Wodarz, Hepatitis C virus dynamics and pathology: The role of CTL and antibody responses, J. Gen. Virol., 84 (2003), 1743–1750. https://doi.org/10.1099/vir.0.19118-0 doi: 10.1099/vir.0.19118-0
[9]	J. Yang, L. Wang, Dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response, Acta Math. Scientia, 41 (2021), 991–1016. https://doi.org/10.1007/s10473-021-0322-y doi: 10.1007/s10473-021-0322-y
[10]	Z. Zhang, Y. Chen, X. Wang, L. Rong, Dynamic analysis of a latent HIV infection model with CTL immune and antibody responses, Int. J. Biomath., 17 (2024), 2350079. https://doi.org/10.1142/S1793524523500791 doi: 10.1142/S1793524523500791
[11]	P. Balasubramaniam, P. Tamilalagan, M. Prakash, Bifurcation analysis of HIV infection model with antibody and cytotoxic T-lymphocyte immune responses and Beddington-DeAngelis functional response, Math. Methods Appl. Sci., 38 (2015), 1330–1341. https://doi.org/10.1002/mma.3148 doi: 10.1002/mma.3148
[12]	C. M. Card, W. J. Rutherford, S. Ramdahin, X. Yao, M. Kimani, C. Wachihi, et al., Reduced cellular susceptibility to in vitro HIV infection is associated with CD4+ T cell quiescence, PLoS ONE, 7 (2012), e45911. https://doi.org/10.1371/journal.pone.0045911 doi: 10.1371/journal.pone.0045911
[13]	I. Nali, A. Dénes, A. Tridane, X. Zhou, Dynamical analysis of an hiv infection model including quiescent cells and immune response, Math. Methods Appl. Sci., 48 (2025), 14301–14315. https://doi.org/10.1002/mma.11179 doi: 10.1002/mma.11179
[14]	A. Singh, B. Razooky, C. D. Cox, M. L. Simpson, L. S. Weinberger, Transcriptional bursting from the HIV-1 promoter is a significant source of stochastic noise in HIV-1 gene expression, Biophys. J., 98 (2010), L32–L34. https://doi.org/10.1016/j.bpj.2010.03.001 doi: 10.1016/j.bpj.2010.03.001
[15]	H. C. Tuckwell, E. Le Corfec, A stochastic model for early HIV-1 population dynamics, J. Theor. Biol., 195 (1998), 451–463. https://doi.org/10.1006/jtbi.1998.0806 doi: 10.1006/jtbi.1998.0806
[16]	N. Dalal, D. Greenhalgh, X. Mao, A stochastic model for internal HIV dynamics, J. Math. Anal. Appl., 341 (2008), 1084–1101. https://doi.org/10.1016/j.jmaa.2007.11.005 doi: 10.1016/j.jmaa.2007.11.005
[17]	Y. Cheng, M. Li, F. Zhang, A dynamics stochastic model with HIV infection of CD4$^+$ T-cells driven by Lévy noise, Chaos Soliton Fract., 129 (2019), 62–70. https://doi.org/10.1016/j.chaos.2019.07.054 doi: 10.1016/j.chaos.2019.07.054
[18]	Y. Wang, M. Lu, D. Jiang, Dynamic behavior of a general stochastic HIV model with virus-to-cell infection, cell-to-cell transmission, immune response and distributed delays, J. Nonlinear Sci., 33 (2023), 97. https://doi.org/10.1007/s00332-023-09955-5 doi: 10.1007/s00332-023-09955-5
[19]	J. X. Shang, D. Li, D. H. He, Z. Jin, H. T. Song, Dynamical Analysis of a stochastic dual-strain infectious model with hospital beds and logarithmic Ornstein-Uhlenbeck Process, J. Math. Biol., 93 (2026), 16. https://doi.org/10.1007/s00285-026-02434-x doi: 10.1007/s00285-026-02434-x
[20]	Q. Liu, D. Jiang, T. Hayat, A. Alsaedi, Stationary distribution and extinction of a stochastic HIV-1 infection model with distributed delay and logistic growth, J. Nonlinear Sci., 30 (2020), 369–395. https://doi.org/10.1007/s00332-019-09576-x doi: 10.1007/s00332-019-09576-x
[21]	R. Khashminski, Stochastic Stability of Differential Equations, Berlin: Springer-Verlag, 1980. https://doi.org/10.1007/978-94-009-9121-7
[22]	X. Mao, Stochastic Differential Equations and Their Applications, Horwood, Chichester, 1997.
[23]	Y. Zhou, W. Zhang, Threshold of a stochastic SIR epidemic model with Lévy jumps, Phys. A, 446 (2016), 204–216. https://doi.org/10.1016/j.physa.2015.11.023 doi: 10.1016/j.physa.2015.11.023
[24]	D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001), 525–546. https://doi.org/10.1137/S0036144500378302 doi: 10.1137/S0036144500378302
[25]	Y. Tan, S. Liu, Y. Cai, X. Sun, R. Yao, D. He, et al., Stochastic modeling and optimal control of HIV-1 infection dynamics under combination antiretroviral therapy, Bull. Math. Biol., 88 (2026), 20. https://doi.org/10.1007/s11538-025-01586-z doi: 10.1007/s11538-025-01586-z
[26]	R. T. Gandhi, R. J. Landovitz, P. E. Sax, D. M. Smith, S. A. Springer, H. F. Günthard, et al., Antiretroviral drugs for treatment and prevention of HIV in adults: 2024 recommendations of the international antiviral society-USA panel, JAMA, 333 (2025), 609–628. https://doi.org/10.1001/jama.2024.24543 doi: 10.1001/jama.2024.24543
[27]	J. Wang, J. Pang, T. Kuniya, Y. Enatsu, Global threshold dynamics in a five-dimensional virus model with cell-mediated, humoral immune responses and distributed delays, Appl. Math. Comput., 241 (2014), 298–316. https://doi.org/10.1016/j.amc.2014.05.015 doi: 10.1016/j.amc.2014.05.015
[28]	J. Ren, R. Xu, L. Li, Global stability of an HIV infection model with saturated CTL immune response and intracellular delay, Math. Biosci. Eng., 18 (2021), 57–68. https://doi.org/10.3934/mbe.2021003 doi: 10.3934/mbe.2021003
[29]	M. Kouche, B. Boulfoul, B. E. Ainseba, Mathematical analysis of an HIV infection model including quiescent cells and periodic antiviral therapy, Int. J. Biomath., 10 (2017), 1750065. https://doi.org/10.1142/S1793524517500656 doi: 10.1142/S1793524517500656
[30]	M. Lavielle, A. Samson, A. Karina Fermin, F. Mentré, Maximum likelihood estimation of long-term HIV dynamic models and antiviral response, Biometrics, 67 (2011), 250–259. https://doi.org/10.1111/j.1541-0420.2010.01422.x doi: 10.1111/j.1541-0420.2010.01422.x

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