IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i17p2735-d1469112.html
   My bibliography  Save this article

Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate

Author

Listed:
  • Juhui Yan

    (School of Mathematics and Computer Science, Yunnan Minzu University, Yuehua Street No. 2929, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Wanqin Wu

    (School of Mathematics and Computer Science, Yunnan Minzu University, Yuehua Street No. 2929, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Qing Miao

    (School of Mathematics and Computer Science, Yunnan Minzu University, Yuehua Street No. 2929, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Xuewen Tan

    (School of Mathematics and Computer Science, Yunnan Minzu University, Yuehua Street No. 2929, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

Abstract

This paper performs a detailed analysis and explores optimal control strategies for a fractional-order SIV epidemic model, incorporating a nonmonotonic incidence rate. In this paper, the population of vaccinated individuals is included in the disease dynamics model. After proving the non-negative boundedness of the fractional-order SIV model, we focus on analyzing the equilibrium point characteristics of the model, delving into its existence, uniqueness, and stability analysis. In addition, our research includes formulating optimal control strategies specifically aimed at minimizing the number of infections while keeping costs as low as possible. To validate the theoretical findings and uncover the practical efficacy and prospects of control measures in mitigating epidemic spread, numerical simulations are performed.

Suggested Citation

  • Juhui Yan & Wanqin Wu & Qing Miao & Xuewen Tan, 2024. "Global Dynamics and Optimal Control of a Fractional-Order SIV Epidemic Model with Nonmonotonic Occurrence Rate," Mathematics, MDPI, vol. 12(17), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2735-:d:1469112
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/17/2735/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/17/2735/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    2. Memon, Zaibunnisa & Qureshi, Sania & Memon, Bisharat Rasool, 2021. "Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Vargas-De-León, Cruz, 2011. "On the global stability of SIS, SIR and SIRS epidemic models with standard incidence," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1106-1110.
    4. Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
    5. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Phukan, Jyotiska & Dutta, Hemen, 2023. "Dynamic analysis of a fractional order SIR model with specific functional response and Holling type II treatment rate," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Parsamanesh, Mahmood & Erfanian, Majid, 2021. "Stability and bifurcations in a discrete-time SIVS model with saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Ameen, I. & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2020. "An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 137(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. Abboubakar, Hamadjam & Kombou, Lausaire Kemayou & Koko, Adamou Dang & Fouda, Henri Paul Ekobena & Kumar, Anoop, 2021. "Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Liu, Na & Wang, Jia & Sun, Junwei & Zhang, Chong & Lan, Qixun & Deng, Wei, 2025. "Dynamical analysis of a fractional-order epidemic weighted network model and its finite-time control," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    3. Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    4. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    5. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Shoaib, Muhammad & Kiani, Adiqa Kausar, 2022. "Fractional order Lorenz based physics informed SARFIMA-NARX model to monitor and mitigate megacities air pollution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Yanfang Liang & Wenlong Wang, 2025. "Dynamic Properties and Chaos Control Analysis of Discrete Epidemic Models Affected by Media Coverage," Mathematics, MDPI, vol. 13(17), pages 1-17, September.
    7. Talal Daghriri & Michael Proctor & Sarah Matthews, 2022. "Evolution of Select Epidemiological Modeling and the Rise of Population Sentiment Analysis: A Literature Review and COVID-19 Sentiment Illustration," IJERPH, MDPI, vol. 19(6), pages 1-20, March.
    8. Fatima, Bibi & Zaman, Gul, 2020. "Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Hegagi Mohamed Ali & Saud Owyed & Ismail Gad Ameen, 2025. "Fractional Optimal Control Problem and Stability Analysis of Rumor Spreading Model with Effective Strategies," Mathematics, MDPI, vol. 13(11), pages 1-25, May.
    10. Leul Mekonnen Anteneh & Mahouton Norbert Hounkonnou & Romain Glèlè Kakaï, 2025. "A Stochastic Continuous-Time Markov Chain Approach for Modeling the Dynamics of Cholera Transmission: Exploring the Probability of Disease Persistence or Extinction," Mathematics, MDPI, vol. 13(6), pages 1-26, March.
    11. Yifeng Liu & Yuan Lai, 2024. "Analyzing jogging activity patterns and adaptation to public health regulation," Environment and Planning B, , vol. 51(3), pages 670-688, March.
    12. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    13. Batabyal, Saikat, 2021. "COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    14. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 684-704.
    15. Hoang, Manh Tuan & Pham, Hoai Thu, 2025. "Global dynamics and numerical simulation of a modified epidemiological model for viral marketing on social networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 225-244.
    16. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    17. El-Mesady, A. & Ali, Hegagi Mohamed, 2024. "The influence of prevention and isolation measures to control the infections of the fractional Chickenpox disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 606-630.
    18. Utsumi, Shinobu & Arefin, Md. Rajib & Tatsukawa, Yuichi & Tanimoto, Jun, 2022. "How and to what extent does the anti-social behavior of violating self-quarantine measures increase the spread of disease?," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    19. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    20. Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:12:y:2024:i:17:p:2735-:d:1469112. 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.