IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v138y2017icp31-48.html
   My bibliography  Save this article

Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays

Author

Listed:
  • Wang, Yan
  • Liu, Xianning

Abstract

In this paper, a within-host chikungunya virus infection model with two delays is considered. The basic reproductive number R0 is formulated. If R0<1, the virus-free equilibrium is globally asymptotically stable and the disease always dies out. If R0>1, the global stability of the unique endemic equilibrium E1 is proved for the case without the time delay of antigenic stimulation, which can change the stability of E1 and lead to the existence of Hopf bifurcation. Furthermore, explicit formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are established. Finally, some numerical simulations are presented to illustrate the results.

Suggested Citation

  • Wang, Yan & Liu, Xianning, 2017. "Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 31-48.
    • Handle: RePEc:eee:matcom:v:138:y:2017:i:c:p:31-48
    DOI: 10.1016/j.matcom.2016.12.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475417300101
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2016.12.011?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. Laith Yakob & Archie C A Clements, 2013. "A Mathematical Model of Chikungunya Dynamics and Control: The Major Epidemic on Réunion Island," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-6, March.
    2. Wang, Tianlei & Hu, Zhixing & Liao, Fucheng & Ma, Wanbiao, 2013. "Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 13-22.
    3. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
    4. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed M. Elaiw & Aeshah A. Raezah & Matuka A. Alshaikh, 2023. "Global Dynamics of Viral Infection with Two Distinct Populations of Antibodies," Mathematics, MDPI, vol. 11(14), pages 1-26, July.
    2. Salah Alsahafi & Stephen Woodcock, 2021. "Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate," Mathematics, MDPI, vol. 9(18), pages 1-18, September.
    3. Ahmed M. Elaiw & Taofeek O. Alade & Saud M. Alsulami, 2018. "Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells," Mathematics, MDPI, vol. 6(7), pages 1-19, July.
    4. De Cesare, Luigi & Sportelli, Mario, 2020. "Stability and direction of Hopf bifurcations of a cyclical growth model with two-time delays and one-delay dependent coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. A. M. Elaiw & N. H. AlShamrani & E. Dahy & A. A. Abdellatif & Aeshah A. Raezah, 2023. "Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection," Mathematics, MDPI, vol. 11(3), pages 1-26, January.
    6. 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.
    7. Wang, Yan & Li, Yazhi & Liu, Lili & Liu, Xianning, 2022. "A periodic Chikungunya model with virus mutation and transovarial transmission," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

    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. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    2. Sun, Hongquan & Li, Jin, 2020. "A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Thirthar, Ashraf Adnan & Majeed, Salam J. & Alqudah, Manar A. & Panja, Prabir & Abdeljawad, Thabet, 2022. "Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar, 2015. "Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1072-1094.
    5. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    6. 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.
    7. Miao, Hui & Abdurahman, Xamxinur & Teng, Zhidong & Zhang, Long, 2018. "Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 280-291.
    8. Kim, Kwang Su & Kim, Sangil & Jung, Il Hyo, 2018. "Hopf bifurcation analysis and optimal control of Treatment in a delayed oncolytic virus dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 1-16.
    9. 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).
    10. Bürger, Raimund & Ruiz-Baier, Ricardo & Tian, Canrong, 2017. "Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 28-52.
    11. 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).
    12. Sharma, Naveen & Singh, Ram & Singh, Jagdev & Castillo, Oscar, 2021. "Modeling assumptions, optimal control strategies and mitigation through vaccination to Zika virus," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    13. Sun, Dandan & Teng, Zhidong & Wang, Kai & Zhang, Tailei, 2023. "Stability and Hopf bifurcation in delayed age-structured SVIR epidemic model with vaccination and incubation," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    14. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    15. Geng, Yan & Xu, Jinhu & Hou, Jiangyong, 2018. "Discretization and dynamic consistency of a delayed and diffusive viral infection model," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 282-295.
    16. Wang, Xia & Song, Xinyu & Tang, Sanyi & Rong, Libin, 2016. "Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 87-103.
    17. Pati, N.C. & Ghosh, Bapan, 2022. "Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 171-196.
    18. Lin, Jiazhe & Xu, Rui & Tian, Xiaohong, 2017. "Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 516-530.
    19. Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.
    20. Yang, Yu & Ye, Jin, 2009. "Hopf bifurcation in a predator–prey system with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 554-559.

    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:matcom:v:138:y:2017:i:c:p:31-48. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.