IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v169y2023ics0960077923002242.html
   My bibliography  Save this article

Global approximate solution of SIR epidemic model with constant vaccination strategy

Author

Listed:
  • Chakir, Yassine

Abstract

Providing a global semi-analytical method has the advantage of offering a global and accurate solution to the epidemic model, which can help in studying and controlling the spread of the disease. Unlike numerical methods such as the Runge–Kutta–Fehlberg method, global semi-analytical methods can provide an explicit expression of the solution over the entire time period, including obtaining the peak time, which is crucial information for understanding disease spread. In this paper, a global semi-analytical method based on the two-point Padé approximants for solving the SIR epidemic model of childhood diseases is presented. The objective of this study is to examine the temporal dynamics of a childhood disease when a preventive vaccine is present. For this purpose, we have first derived the solution of the SIR model of childhood diseases in terms of series expansions for small and large values. Then, the theory of two-point Padé approximations is used to provide the global approximate solution. The peak time related to this model is also obtained via these global approximants. Furthermore, in order to show the efficiency of our study, some graphs have been given to compare our results with those obtained using the classical Padé approximations and the numerical Runge–Kutta–Fehlberg method.

Suggested Citation

  • Chakir, Yassine, 2023. "Global approximate solution of SIR epidemic model with constant vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923002242
    DOI: 10.1016/j.chaos.2023.113323
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923002242
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113323?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. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Ding Chen, 2020. "On the Integrability of the SIR Epidemic Model with Vital Dynamics," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-10, July.
    3. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2021. "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 514-534.
    4. Turkyilmazoglu, Mustafa, 2022. "An extended epidemic model with vaccination: Weak-immune SIRVI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(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. Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    2. Hernández, G. & Martín del Rey, A., 2022. "Community-distributed compartmental models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    3. 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).
    4. Fehaid Salem Alshammari & Fahir Talay Akyildiz, 2023. "Epidemic Waves in a Stochastic SIRVI Epidemic Model Incorporating the Ornstein–Uhlenbeck Process," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    5. Vivekanandhan, Gayathri & Nourian Zavareh, Mahdi & Natiq, Hayder & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Svetec, Milan, 2022. "Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    6. Turkyilmazoglu, Mustafa, 2022. "A restricted epidemic SIR model with elementary solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    7. Zhu, Hongmiao & Jin, Zhen, 2023. "A dynamics model of knowledge dissemination in a WeChat Group from perspective of duplex networks," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    8. Jang, Gyeong Hwan & Kim, Sung Jin & Lee, Mi Jin & Son, Seung-Woo, 2024. "Effectiveness of vaccination and quarantine policies to curb the spread of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    9. Saha, Sangeeta & Dutta, Protyusha & Samanta, Guruprasad, 2022. "Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(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:eee:chsofr:v:169:y:2023:i:c:s0960077923002242. 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.