Analysis of delayed HIV-1 dynamics model with inflammatory cytokines and cellular infection

Volume 35, Issue 1, pp 52--81 https://dx.doi.org/10.22436/jmcs.035.01.05

Publication Date: April 17, 2024 Submission Date: December 28, 2023 Revision Date: January 27, 2024 Accteptance Date: March 10, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 55 Downloads
• 158 Views

Authors

A. A. Raezah - Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia. A. M. Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt. E. Dahy - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt. N. H. Alshamrani - Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia. H. Z. Zidan - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt. A. A. Abdellatif - Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt.

Abstract

The purpose of this research is to develop a mathematical model to study the dynamics of human immunodeficiency virus type-1 (HIV-1) infection with inflammatory cytokines. The model incorporates two modes of infection (viral and cellular), two immune responses (antibody and cytotoxic T lymphocyte (CTL)) and two types of distributed-time delays. We demonstrate that the model's solutions are non-negative and eventually bounded, demonstrating the suggested model's biological viability. We find the equilibrium points of the model and get the sufficient conditions for their existence and stability. The Lyapunov approach is utilized to investigate the global stability of the equilibria. We determine which parameters most affect the basic reproduction number using sensitivity analysis. We reformulate our model by including the influence of three classes of antiretroviral drug therapies. We determine a critical efficacy for each antiretroviral therapy, after which HIV-1 will be eradicated entirely if treatment effectiveness surpasses this threshold. We also establish that the estimated treatment efficacy will be lower than what is necessary to eliminate the virus entirely if the inflammatory cytokines and/or cellular infection are ignored. Moreover, we show that time delay has an identical effect on virus elimination as antiretroviral therapy. It is also shown that, prolonging time delays can successfully reduce the basic reproduction number and stop HIV-1 replication. According to our findings, time delay, cellular infection, and inflammatory cytokines are crucial components of the HIV-1 model and should not be disregarded. The study's analytical and numerical findings advance our knowledge of HIV-1 dynamics and may help develop more effective HIV-1 management plans.

Share and Cite

Keywords

• HIV-1
• inflammatory cytokines
• viral and cellular infections
• immune response
• time delay
• global stability
• Lyapunov method

MSC

•  34D20
•  34D23
•  37N25
•  92B05

References

• [1] Stability of HIV/HTLV co-infection model with effective HIV-specific antibody immune response, M. A. Alshaikh, N. H. AlShamrani, A. M. Elaiw, Results Phys., 27 (2021), 24 pages
  • View Article
  • Google Scholar


• [2] N. Bellomo, D. Burini, N. Outada, Multiscale models of COVID-19 with mutations and variants, Netw. Heterog. Media, 17 (2022), 293–310
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] D. S. Callaway, A. S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol., 64 (2002), 29–64
  • View Article
  • Google Scholar
  • MATH


• [4] A. N. Chatterjee, F. Al Basir, M. A. Almuqrin, J. Mondal, I. Khan, SARS-CoV-2 infection with lytic and nonlytic immune responses: a fractional order optimal control theoretical study, Results Phys., 6 (2021), 9 pages
  • View Article
  • Google Scholar


• [5] C. Chen, Z. Ye, Y. Zhou, Z. Zheng, Dynamics of a delayed cytokine-enhanced diffusive HIV model with a general incidence and CTL immune response, Eur. Phys. J. Plus, 138 (2023),
  • View Article
  • Google Scholar


• [6] C. Chen, Y. Zhou, Dynamic analysis of HIV model with a general incidence, CTLs immune response and intracellular delays, Math. Comput. Simulation, 212 (2023), 159–181
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] C. Chen, Y. Zhou, Z. Ye, Stability and optimal control of a cytokine-enhanced general HIV infection model with antibody immune response and CTLs immune response, Comput. Methods Biomech. Biomed. Engin., (2023), 1–32
  • View Article
  • Google Scholar


• [8] R. V. Culshaw, S. Ruan, G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol., 46 (2003), 425–444
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] E. Dahy, A. M. Elaiw, A. A. Raezah, H. Z. Zidan, A. E. A. Abdellatif, Global properties of cytokine-enhanced HIV-1 dynamics model with adaptive immunity and distributed delays, Computation, 11 (2023), 36 pages
  • View Article
  • Google Scholar


• [10] J. Deng, H. Shu, L. Wang, X.-S. Wang, Viral dynamics with immune responses: effects of distributed delays and Filippov antiretroviral therapy, , 86 (2023), 29 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] M. Dhar, S. Samaddar, P. Bhattacharya, Modeling the effect of non-cytolytic immune response on viral infection dynamics in the presence of humoral immunity, Nonlinear Dyn., 98 (2019), 637–655
  • View Article
  • Google Scholar
  • MATH


• [12] G. Doitsh, N. L. K. Galloway, X. Geng, Z. Yang, K. M. Monroe, O. Zepeda, P. W. Hunt, H. Hatano, S. Sowinski, I. Mu˜ noz-Arias, W. C. Greene, Cell death by pyroptosis drives CD4 T-cell depletion in HIV-1 infection, Nature, 505 (2014), 509–514
  • View Article
  • Google Scholar


• [13] A. M. Elaiw, R. M. Abukwaik, E. O. Alzahrani, Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays, Int. J. Biomath., 7 (2014), 25 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] A. M. Elaiw, A. D. Al Agha, Analysis of a delayed and diffusive oncolytic M1 virotherapy model with immune response, Nonlinear Anal. Real World Appl., 55 (2020), 32 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] A. M. Elaiw, N. H. AlShamrani, Global stability of a delayed adaptive immunity viral infection with two routes of infection and multi-stages of infected cells, Commun. Nonlinear Sci. Numer. Simul., 86 (2020), 27 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] A. M. Elaiw, N. H. AlShamrani, HTLV/HIV dual Infection: Modeling and analysis, Mathematics, 9 (2021), 32 pages
  • View Article
  • Google Scholar


• [17] A. M. Elaiw, N. H. AlShamrani, Stability of HIV/HTLV-I co-infection model with delays, Math. Methods Appl. Sci., 45 (2022), 238–300
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] A. M. Elaiw, N. H. AlShamrani, A. D. Hobiny, Stability of an adaptive immunity delayed HIV infection model with active and silent cell-to-cell spread, Math. Biosci. Eng., 17 (2020), 6401–6458
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] Y. Gao, J. Wang, Threshold dynamics of a delayed nonlocal reaction-diffusion HIV infection model with both cell-free and cell-to-cell transmissions, J. Math. Anal. Appl., 488 (2020), 21 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] T. Guo, Z. Qiu, L. Rong, Analysis of an HIV model with immune responses and cell-to-cell transmission, Bull. Malays. Math. Sci. Soc., 43 (2020), 581–607
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] J. K. Hale, S. M. V. Lunel, Introduction to functional differential equations, Springer-Verlag, New York (1993)
  • View Article
  • MathSciNet
  • Google Scholar


• [22] K. Hattaf, N. Yousfi, Modeling the adaptive immunity and both modes of transmission in HIV infection, Computation, 6 (2018), 18 pages
  • View Article
  • Google Scholar


• [23] Z. Hemmatzadeh, V. Roomi, T. K. Gharahasanlou, Stability, Hopf bifurcation and numerical simulation of an HIV model with two modes of transmission and with cellular and humoral immunity, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 33 (2023), 19 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [24] Y. Jiang, T. Zhang, Global stability of a cytokine-enhanced viral infection model with nonlinear incidence rate and time delays, Appl. Math. Lett., 132 (2022), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] C. Jolly, Q. Sattentau, Retroviral spread by induction of virological synapses, Traffic, 5 (2004), 643–650
  • View Article
  • Google Scholar


• [26] H. K. Khalil, Control of nonlinear systems, Prentice Hall, New York (202)
  • View Article
  • Google Scholar


• [27] N. L. Komarova, D. Wodarz, Virus dynamics in the presence of synaptic transmission, Math. Biosci., 242 (2013), 161–171
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [28] A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879–883
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [29] Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, Boston (1993)
  • View Article
  • Google Scholar


• [30] F. Li, W. Ma, Dynamics analysis of an HTLV-1 infection model with mitotic division of actively infected cells and delayed CTL immune response, Math. Methods Appl. Sci., 41 (2018), 3000–3017
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [31] J. Li, X. Wang, Y. Chen, Analysis of an age-structured HIV infection model with cell-to-cell transmission, Eur. Phys. J. Plus, 139 (2024),
  • View Article
  • Google Scholar


• [32] J. Lin, R. Xu, X. Tian, Threshold dynamics of an HIV-1 model with both viral and cellular infections, cell-mediated and humoral immune responses, Math. Biosci. Eng., 16 (2018), 292–319
  • View Article
  • Google Scholar
  • MATH


• [33] S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theoret. Biol., 254 (2008), 178–196
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [34] H. Mohri, S. Bonhoeffer, S. Monard, A. S. Perelson, D. D. Ho, Rapid turnover of T lymphocytes in SIV-infected rhesus macaques, Science, 279 (1998), 1223–1227
  • View Article
  • Google Scholar


• [35] Z. Monfared, F. Omidiy Y. Qaseminezhad Raeiniz, Investigating the effect of pyroptosis on the slow CD4+ T cell depletion in HIV-1 infection, by dynamical analysis of its discontinuous mathematical model, Int. J. Biomath., 13 (2020), 23 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [36] A. Murase, T. Sasaki, T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, J. Math. Biol., 51 (2005), 247–267
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [37] Y. Nakata, Global dynamics of a cell mediated immunity in viral infection models with distributed delays, J. Math. Anal. Appl., 375 (2011), 14–27
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [38] B. J. Nath, K. Sadri, H. K. Sarmah, K. Hosseini, An optimal combination of antiretroviral treatment and immunotherapy for controlling HIV infection, Math. Comput. Simulation, 217 (2024), 226–243
  • View Article
  • MathSciNet
  • Google Scholar


• [39] M. A. Nowak, C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74–79
  • View Article
  • Google Scholar


• [40] M. A. Nowak, R. M. May, Virus Dynamics, Oxford University Press, Oxford (2000)
  • View Article


• [41] A. S. Perelson, D. E. Kirschner, R. De Boer, Dynamics of HIV Infection of CD4+ T cells, Math. Biosci., 114 (1993), 81–125
  • View Article
  • Google Scholar


• [42] A. Perelson, A. Neumann, M. Markowitz, J. Leonard, D. Ho, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, 271 (1996), 1582–1586
  • View Article
  • Google Scholar


• [43] J. K. Rathkey, J. Zhao, Z. Liu, Y. Chen, J. Yang, H. C. Kondolf, B. L. Benson, S. M. Chirieleison, A. Y. Huang, G. R. Dubyak, T. S. Xiao, X. Li, D. W. Abbott, Chemical disruption of the pyroptotic pore-forming protein gasdermin D inhibits inflammatory cell death and sepsis, Sci. Immunol., 3 (2018), 11 pages
  • View Article
  • Google Scholar


• [44] A. Sigal, J. T. Kim, A. B. Balazs, E. Dekel, A. Mayo, R. Milo, D. Baltimore, Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy, Nature, 477 (2011), 95–98
  • View Article
  • Google Scholar


• [45] S. Tang, Z. Teng, H. Miao, Global dynamics of a reaction–diffusion virus infection model with humoral immunity and nonlinear incidence, Comput. Math. Appl., 78 (2019), 786–806
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [46] W. Wang, Mean-square exponential input-to-state stability of stochastic fuzzy delayed Cohen-Grossberg neural networks, J. Exp. Theor. Artif. Intell., (2023), 1–14
  • View Article
  • Google Scholar


• [47] W. Wang, Z. Feng, Global dynamics of a diffusive viral infection model with spatial heterogeneity, Nonlinear Anal. Real World Appl., 72 (2023), 21 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [48] J. Wang, M. Guo, X. Liu, Z. Zhao, Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Appl. Math. Comput., 291 (2016), 149–161
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [49] S. Wang, P. Hottz, M. Schechter, L. Rong, Modeling the slow CD4 + T cell decline in HIV-infected individuals, PLoS Comput. Biol., 11 (2015), 25 pages
  • View Article
  • Google Scholar


• [50] W. Wang, W. Ma, Z. Feng, Complex dynamics of a time periodic nonlocal and time-delayed model of reaction-diffusion equations for modelling CD4 + T cells decline, J. Comput. Appl. Math., 367 (2020), 29 pages
  • View Article
  • Google Scholar


• [51] 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
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [52] W. Wang, X. Ren, W. Ma, X. Lai, New insights into pharmacologic inhibition of pyroptotic cell death by necrosulfonamide: A PDE model, Nonlinear Anal. Real World Appl., 56 (2020), 21 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [53] W. Wang, X. Ren, X. Wang, Spatial-temporal dynamics of a novel PDE model: applications to pharmacologic inhibition of pyroptosis by necrosulfonamide, Commun. Nonlinear Sci. Numer. Simul., 103 (2021), 18 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [54] X. Wang, L. Rong, HIV low viral load persistence under treatment: Insights from a model of cell-to-cell viral transmission, Appl. Math. Lett., 94 (2019), 44–51
  • View Article
  • Google Scholar


• [55] W. Wang, T. Zhang, Caspase-1-mediated pyroptosis of the predominance for driving CD4+ T cells death: a nonlocal spatial mathematical model, Bull. Math. Biol., 80 (2018), 540–582
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [56] Y. Wang, Y. Zhou, F. Brauer, J. M. Heffernan, Viral dynamics model with CTL immune response incorporating antiretroviral therapy, J. Math. Biol., 67 (2013), 901–934
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [57] S. Wang, D. Zou, Global stability of in host viral models with humoral immunity and intracellular delays, Appl. Math. Model., 36 (2012), 1313–1322
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [58] D. Wodarz, R. M. May, M. A. Nowak, The role of antigen-independent persistence of memory cytotoxic T lymphocytes, Int. Immunol., 12 (2000), 467–477
  • View Article
  • Google Scholar


• [59] D. Wodarz, Hepatitis C virus dynamics and pathology: The role of CTL and antibody responses, J. Gen. Virol., 84 (2003), 1743–1750
  • View Article
  • Google Scholar


• [60] R. Xu, Global dynamics of an HIV-1 infection model with distributed intracellular delays, Comput. Math. Appl., 61 (2011), 2799–2805
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [61] J. Xu, Dynamic analysis of a cytokine-enhanced viral infection model with infection age, Math. Biosci. Eng., 20 (2023), 8666–8684
  • View Article
  • MathSciNet
  • Google Scholar


• [62] Y. Yan, W. Wang, Global stability of a five-dimensional model with immune responses and delay, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), 401–416
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [63] H. Yang, X. Li, W. Zhang, A stochastic HIV/HTLV-I co-infection model incorporating the AIDS-related cancer cells, Discrete Contin. Dyn. Syst. Ser. B, 29 (2024), 702–730
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [64] J. Yang, L. Wang, Dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response, Acta Math. Sci. Ser. B (Engl. Ed.), 41 (2021), 991–1016
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [65] T. Zhang, X. Xu, X. Wang, Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response, Chaos Solitons Fractals, 170 (2023), 15 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [66] 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), 28 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [67] T. Zheng, Y. Luo, Z. Teng, Spatial dynamics of a viral infection model with immune response and nonlinear incidence, Z. Angew. Math. Phys., 74 (2023), 32 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH