IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923008007.html
   My bibliography  Save this article

Bifurcation analysis and optimal control of discrete SIR model for COVID-19

Author

Listed:
  • Ahmed, Mostak
  • Masud, Md. Abdullah Bin
  • Sarker, Md. Manirul Alam

Abstract

Our research focuses on studying a COVID-19 SIR model for discrete cases, incorporating bi-linear phenomena and a constant rate of recovery. We have interested in analyzing the conditions for the existence of disease-free equilibrium and local equilibrium in this model. Additionally, we are investigating the stability of several bifurcations, including saddle–node bifurcations, flip bifurcations, 1:1 resonances, and Neimark-Sacker bifurcations. These bifurcations provide insights into the behavior and dynamics of the system as specific parameters change. We propose a vaccine response rate to introduce a control variable for the SIR system. This variable represents the rate at which individuals receive vaccinations, which can affect the spread of the disease. Finally, demonstrate an epidemic model based on vaccination control with social awareness, using the results and insights obtained from our analysis to showcase the effectiveness of the proposed control strategy in mitigating the spread of COVID-19. In our research, we also employ Pontryagin’s maximum principle to solve the system. By applying this principle, we can determine the optimal control strategy that minimizes the spread of the disease or achieves other desired objectives. We have conducted a comprehensive analysis of the COVID-19 SIR model with a focus on bifurcations, control strategies, and social awareness about the impact of vaccination. Such research contributes to our understanding of the dynamics of infectious diseases and provides valuable insights for controlling epidemics.

Suggested Citation

  • Ahmed, Mostak & Masud, Md. Abdullah Bin & Sarker, Md. Manirul Alam, 2023. "Bifurcation analysis and optimal control of discrete SIR model for COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923008007
    DOI: 10.1016/j.chaos.2023.113899
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008007
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113899?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. Kada, Driss & Kouidere, Abdelfatah & Balatif, Omar & Rachik, Mostafa & Labriji, El Houssine, 2020. "Mathematical modeling of the spread of COVID-19 among different age groups in Morocco: Optimal control approach for intervention strategies," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Omar Zakary & Sara Bidah & Mostafa Rachik & Hanane Ferjouchia, 2020. "Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-13, October.
    3. Gondim, João A.M. & Machado, Larissa, 2020. "Optimal quarantine strategies for the COVID-19 pandemic in a population with a discrete age structure," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    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. Rafiq, Muhammad Hamza & Raza, Nauman & Jhangeer, Adil & Zidan, Ahmed M., 2024. "Qualitative analysis, exact solutions and symmetry reduction for a generalized (2＋1)-dimensional KP–MEW-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(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. Protyusha Dutta & Nirapada Santra & Guruprasad Samanta & Manuel De la Sen, 2024. "Nonlinear SIRS Fractional-Order Model: Analysing the Impact of Public Attitudes towards Vaccination, Government Actions, and Social Behavior on Disease Spread," Mathematics, MDPI, vol. 12(14), pages 1-29, July.
    2. Kouidere, Abdelfatah & Balatif, Omar & Rachik, Mostafa, 2021. "Analysis and optimal control of a mathematical modeling of the spread of African swine fever virus with a case study of South Korea and cost-effectiveness," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Mugnaine, Michele & Gabrick, Enrique C. & Protachevicz, Paulo R. & Iarosz, Kelly C. & de Souza, Silvio L.T. & Almeida, Alexandre C.L. & Batista, Antonio M. & Caldas, Iberê L. & Szezech Jr, José D. & V, 2022. "Control attenuation and temporary immunity in a cellular automata SEIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Kouidere, Abdelfatah & Youssoufi, Lahcen EL & Ferjouchia, Hanane & Balatif, Omar & Rachik, Mostafa, 2021. "Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Khajji, Bouchaib & Kouidere, Abdelfatah & Elhia, Mohamed & Balatif, Omar & Rachik, Mostafa, 2021. "Fractional optimal control problem for an age-structured model of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Raydonal Ospina & João A. M. Gondim & Víctor Leiva & Cecilia Castro, 2023. "An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil," Mathematics, MDPI, vol. 11(14), pages 1-18, July.

    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:174:y:2023:i:c:s0960077923008007. 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.