IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v170y2023ics0960077923002588.html
   My bibliography  Save this article

Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response

Author

Listed:
  • Zhang, Tongqian
  • Xu, Xinna
  • Wang, Xinzeng

Abstract

In this paper, a cytokine-enhanced viral infection model with time delays and CTL immune response is proposed and analyzed. Multiple time delays, namely intracellular delay τ1, virus replication delay τ2 and immune response delay τ3 are included. Firstly, two key parameters with strong biological significance, namely the virus reproductive number R0 and the CTL immune reproductive number R1 are derived. And then the stability of equilibria of the model is investigated by constructing suitable Lyapunov functionals and using LaSalle’s invariance principle. We prove that if R0<1, then the infection-free equilibrium E0 is globally asymptotically stable for any τ1,τ2,τ3≥0; if R0>1,R1<1, then the immunity-inactivated equilibrium E1 is globally asymptotically stable for any τ1,τ2,τ3≥0; and if R1>1, then the immunity-activated equilibrium E∗ is globally asymptotically stable for any τ1,τ2≥0 and τ3=0. For τ1,τ2≥0,τ3>0, theoretical analysis and numerical simulations show that with the increase of τ3, the equilibrium E∗ loses its stability and the system generates Hopf bifurcation, which means the system produces periodic oscillation under certain conditions.

Suggested Citation

  • Zhang, Tongqian & Xu, Xinna & Wang, Xinzeng, 2023. "Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002588
    DOI: 10.1016/j.chaos.2023.113357
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923002588
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113357?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrea L. Cox & Robert F. Siliciano, 2014. "Not-so-innocent bystanders," Nature, Nature, vol. 505(7484), pages 492-493, January.
    2. Bai, Zhenguo & Zhou, Yicang, 2012. "Dynamics of a viral infection model with delayed CTL response and immune circadian rhythm," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1133-1139.
    3. P. Balasubramaniam & M. Prakash & Fathalla A. Rihan & S. Lakshmanan, 2014. "Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4 + T-cells," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-18, August.
    4. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.
    5. Wang, Yan & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "A stochastic HIV infection model with T-cell proliferation and CTL immune response," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 477-493.
    6. Mann Manyombe, M.L. & Mbang, J. & Chendjou, G., 2021. "Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. Jiang, Daqing & Liu, Qun & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed & Xia, Peiyan, 2017. "Dynamics of a stochastic HIV-1 infection model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 706-717.
    8. Gilad Doitsh & Nicole L. K. Galloway & Xin Geng & Zhiyuan Yang & Kathryn M. Monroe & Orlando Zepeda & Peter W. Hunt & Hiroyu Hatano & Stefanie Sowinski & Isa Muñoz-Arias & Warner C. Greene, 2014. "Cell death by pyroptosis drives CD4 T-cell depletion in HIV-1 infection," Nature, Nature, vol. 505(7484), pages 509-514, January.
    9. Jia, Xinjing & Xu, Rui, 2022. "Global dynamics of a delayed HTLV-I infection model with Beddington-DeAngelis incidence and immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Bera, Sovan & Khajanchi, Subhas & Roy, Tapan Kumar, 2022. "Dynamics of an HTLV-I infection model with delayed CTLs immune response," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    2. Qesmi, Redouane & Hammoumi, Aayah, 2020. "A stochastic delay model of HIV pathogenesis with reactivation of latent reservoirs," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    4. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Cheng, Yan & Li, Mingtao & Zhang, Fumin, 2019. "A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 62-70.
    6. Wang, Yan & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2018. "Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 276-292.
    7. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    8. Qi, Haokun & Meng, Xinzhu, 2021. "Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 700-719.
    9. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    10. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    11. Veronika Novotná & Vladěna Štěpánková, 2015. "Parameter Estimation for Dynamic Model of the Financial System," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 63(6), pages 2051-2055.
    12. Huang, Zaitang, 2017. "Positive recurrent of stochastic coral reefs model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 751-761.
    13. Quentin Le Hingrat & Paola Sette & Cuiling Xu & Andrew R. Rahmberg & Lilas Tarnus & Haritha Annapureddy & Adam Kleinman & Egidio Brocca-Cofano & Ranjit Sivanandham & Sindhuja Sivanandham & Tianyu He &, 2023. "Prolonged experimental CD4+ T-cell depletion does not cause disease progression in SIV-infected African green monkeys," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    14. Han, Lili & Song, Sha & Pan, Qiuhui & He, Mingfeng, 2023. "The impact of multiple population-wide testing and social distancing on the transmission of an infectious disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    15. Pan, Sonjoy & Chakrabarty, Siddhartha P., 2022. "Analysis of a reaction–diffusion HCV model with general cell-to-cell incidence function incorporating B cell activation and cure rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 431-450.
    16. Shuang Gao & Hong Zhang & He Li & Tianbo Li & Aobo Du & Xiaoxu Ling & Boqun Cheng & Zhimin Zhang, 2019. "IFI16 is Required for an Oligodeoxynucleotide with CCT Repeats to Induce Type I Interferon Production in U937 Cells," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 19(4), pages 14567-14574, July.
    17. Xu, Jinhu & Geng, Yan & Zhou, Yicang, 2017. "Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 62-83.
    18. Alfifi, H.Y., 2023. "Effects of diffusion and delayed immune response on dynamic behavior in a viral model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    19. Mann Manyombe, M.L. & Mbang, J. & Chendjou, G., 2021. "Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    20. Shi, Zhenfeng & Jiang, Daqing, 2022. "Dynamical behaviors of a stochastic HTLV-I infection model with general infection form and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002588. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.