IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2139-d842821.html
   My bibliography  Save this article

Bistability and Robustness for Virus Infection Models with Nonmonotonic Immune Responses in Viral Infection Systems

Author

Listed:
  • Tengfei Wang

    (School of Mathematics and Statistics, Henan University, Kaifeng 475001, China)

  • Shaoli Wang

    (School of Mathematics and Statistics, Henan University, Kaifeng 475001, China)

  • Fei Xu

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada)

Abstract

Recently, bistable viral infection systems have attracted increased attention. In this paper, we study bistability and robustness for virus infection models with nonmonotonic immune responses in viral infection systems. The results show that the existing transcritical bifurcation undergoes backward or forward bifurcation in viral infection models with nonmonotonic immune responses. Our investigation demonstrates that the backward bifurcation threshold is the elite control threshold. When the immune intensity is greater than the elite control threshold, the virus will be under elite control; when the immune intensity is less than the elite control threshold, the virus may rebound. We also give a new definition of robustness to characterize bistable systems.

Suggested Citation

  • Tengfei Wang & Shaoli Wang & Fei Xu, 2022. "Bistability and Robustness for Virus Infection Models with Nonmonotonic Immune Responses in Viral Infection Systems," Mathematics, MDPI, vol. 10(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2139-:d:842821
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2139/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/12/2139/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bi, Kaiming & Chen, Yuyang & Zhao, Songnian & Ben-Arieh, David & (John) Wu, Chih-Hang, 2020. "A new zoonotic visceral leishmaniasis dynamic transmission model with age-structure," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Chen, Yuyang & Bi, Kaiming & Zhao, Songnian & Ben-Arieh, David & Wu, Chih-Hang John, 2017. "Modeling individual fear factor with optimal control in a disease-dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 531-545.
    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. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Rika Amelia & Nursanti Anggriani & Asep K. Supriatna & Noor Istifadah, 2023. "Analysis and Optimal Control of the Tungro Virus Disease Spread Model in Rice Plants by Considering the Characteristics of the Virus, Roguing, and Pesticides," Mathematics, MDPI, vol. 11(5), pages 1-14, February.
    3. Ihtisham Ul Haq & Numan Ullah & Nigar Ali & Kottakkaran Sooppy Nisar, 2022. "A New Mathematical Model of COVID-19 with Quarantine and Vaccination," Mathematics, MDPI, vol. 11(1), pages 1-21, December.
    4. Yi-Fang Luo & Shu-Ching Yang & Shih-Chieh Hung & Kun-Yi Chou, 2022. "Exploring the Impacts of Preventative Health Behaviors with Respect to COVID-19: An Altruistic Perspective," IJERPH, MDPI, vol. 19(13), pages 1-14, June.
    5. Carmen Legarreta & Manuel De la Sen & Santiago Alonso-Quesada, 2024. "On the Properties of a Newly Susceptible, Non-Seriously Infected, Hospitalized, and Recovered Subpopulation Epidemic Model," Mathematics, MDPI, vol. 12(2), pages 1-34, January.
    6. Muntaser Safan & Alhanouf Altheyabi, 2023. "Mathematical Analysis of an Anthroponotic Cutaneous Leishmaniasis Model with Asymptomatic Infection," Mathematics, MDPI, vol. 11(10), pages 1-19, May.
    7. Shao, Quan & Wang, Hong & Zhu, Pei & Dong, Min, 2021. "Group emotional contagion and simulation in large-scale flight delays based on the two-layer network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

    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:gam:jmathe:v:10:y:2022:i:12:p:2139-:d:842821. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.