IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i14p2232-d1437259.html
   My bibliography  Save this article

Nonlinear SIRS Fractional-Order Model: Analysing the Impact of Public Attitudes towards Vaccination, Government Actions, and Social Behavior on Disease Spread

Author

Listed:
  • Protyusha Dutta

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Nirapada Santra

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Guruprasad Samanta

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Manuel De la Sen

    (Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Bizkaia, Spain)

Abstract

This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the equilibrium points is analyzed. Sensitivity analysis is conducted to calculate and discuss the sensitivity index of various parameters. It has been established that the illness would spread across this system when the basic reproduction number is larger than 1, the system becomes infection-free when the reproduction number lies below its threshold value of 1. Numerical figures depict the effects of positive and negative attitudes towards vaccination to make the system disease-free sooner. A comprehensive study regarding various values of the order of fractional derivatives together with integer-order derivatives has been discussed in the numerical section to obtain some useful insights into the intricate dynamics of the proposed system. The Pontryagin principle is used in the formulation and subsequent discussion of an optimum control issue. The study also reveals the significant role of government actions in controlling the epidemic. A numerical analysis has been conducted to compare the system’s behavior under optimal control and without optimal control, aiming to discern their differences. The policies implemented by the government are regarded as the most adequate control strategy, and it is determined that the execution of control mechanisms considerably diminishes the ailment burden.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2232-:d:1437259
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/14/2232/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/14/2232/
    Download Restriction: no
    ---><---

    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. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model," Mathematics, MDPI, vol. 9(7), pages 1-34, March.
    3. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    4. 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).
    5. Muhammad Azeem & Muhammad Farman & Marwan Abukhaled & Kottakkaran Sooppy Nisar & Ali Akgãœl, 2023. "Epidemiological Analysis Of Human Liver Model With Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-12.
    6. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(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. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    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. Gafiychuk, V. & Datsko, B. & Meleshko, V., 2008. "Analysis of fractional order Bonhoeffer–van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 418-424.
    4. Ricardo Almeida & Agnieszka B. Malinowska & Tatiana Odzijewicz, 2019. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1171-1185, September.
    5. Zu, Chuanjin & Gao, Yanming & Yu, Xiangyang, 2021. "Time fractional evolution of a single quantum state and entangled state," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    7. A. A. M. Arafa & M. Khalil & A. Sayed, 2019. "A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    8. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    9. 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).
    10. Qin, Yuyan & Yang, Lixin & Li, Jia & Li, Mengjiao & Du, Meng Meng, 2024. "A simplicial SSIS epidemic model with the outgoing pressure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 654(C).
    11. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    12. 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).
    13. Hai Zhang & Renyu Ye & Jinde Cao & Ahmed Alsaedi, 2017. "Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses," Complexity, Hindawi, vol. 2017, pages 1-13, September.
    14. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Ardak Kashkynbayev & Fathalla A. Rihan, 2021. "Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay," Mathematics, MDPI, vol. 9(15), pages 1-16, August.
    16. Liang, Song & Wu, Ranchao & Chen, Liping, 2016. "Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 49-62.
    17. Li, Yi Xia & Alshehri, Maryam G. & Algehyne, Ebrahem A. & Ali, Aatif & Khan, Muhammad Altaf & Muhammad, Taseer & Islam, Saeed, 2021. "Fractional study of Huanglongbing model with singular and non- singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    18. Chongyang Liu & Changjun Yu & Zhaohua Gong & Huey Tyng Cheong & Kok Lay Teo, 2023. "Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 798-816, May.
    19. Chen, Wen & Hei, Xindong & Sun, Hongguang & Hu, Dongliang, 2018. "Stretched exponential stability of nonlinear Hausdorff dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 259-264.
    20. Shuai Li & Chengdai Huang & Xinyu Song, 2019. "Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System," Complexity, Hindawi, vol. 2019, pages 1-13, April.

    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:14:p:2232-:d:1437259. 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.