IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2224-d847628.html
   My bibliography  Save this article

A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior

Author

Listed:
  • Noureddine Djenina

    (Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Adel Ouannas

    (Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates)

  • Iqbal M. Batiha

    (Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates
    Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan)

  • Giuseppe Grassi

    (Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy)

  • Taki-Eddine Oussaeif

    (Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Shaher Momani

    (Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates
    Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan)

Abstract

During the broadcast of Coronavirus across the globe, many mathematicians made several mathematical models. This was, of course, in order to understand the forecast and behavior of this epidemic’s spread precisely. Nevertheless, due to the lack of much information about it, the application of many models has become difficult in reality and sometimes impossible, unlike the simple SIR model. In this work, a simple, novel fractional-order discrete model is proposed in order to study the behavior of the COVID-19 epidemic. Such a model has shown its ability to adapt to the periodic change in the number of infections. The existence and uniqueness of the solution for the proposed model are examined with the help of the Picard Lindelöf method. Some theoretical results are established in view of the connection between the stability of the fixed points of this model and the basic reproduction number. Several numerical simulations are performed to verify the gained results.

Suggested Citation

  • Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Taki-Eddine Oussaeif & Shaher Momani, 2022. "A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2224-:d:847628
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2224/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2224/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Viet-Thanh Pham, 2020. "On the Stability of Linear Incommensurate Fractional-Order Difference Systems," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    3. Jalil Rashidinia & Mehri Sajjadian & Jorge Duarte & Cristina Januário & Nuno Martins, 2018. "On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy," Complexity, Hindawi, vol. 2018, pages 1-11, December.
    4. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. 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).
    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. Isra Al-Shbeil & Noureddine Djenina & Ali Jaradat & Abdallah Al-Husban & Adel Ouannas & Giuseppe Grassi, 2023. "A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    2. Abdallah Al-Husban & Noureddine Djenina & Rania Saadeh & Adel Ouannas & Giuseppe Grassi, 2023. "A New Incommensurate Fractional-Order COVID 19: Modelling and Dynamical Analysis," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    3. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Slavi Georgiev & Lubin Vulkov, 2022. "Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19," Mathematics, MDPI, vol. 10(22), pages 1-21, November.
    5. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

    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. 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).
    2. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Fu, Xinjie & Wang, JinRong, 2022. "Dynamic stability and optimal control of SISqIqRS epidemic network," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. 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).
    5. Kaushik Dehingia & Ahmed A. Mohsen & Sana Abdulkream Alharbi & Reima Daher Alsemiry & Shahram Rezapour, 2022. "Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    6. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    8. Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Alotaibi, Naif D., 2021. "A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Batabyal, Saikat, 2021. "COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    10. Yanan Liao & Kai Yang & Hua Wang & Qingtai Xiao, 2022. "An Alternative Approach for Identifying Nonlinear Dynamics of the Cascade Logistic-Cubic System," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    11. 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).
    12. Yin, Xuecheng & Büyüktahtakın, İ. Esra & Patel, Bhumi P., 2023. "COVID-19: Data-Driven optimal allocation of ventilator supply under uncertainty and risk," European Journal of Operational Research, Elsevier, vol. 304(1), pages 255-275.
    13. Kang, Daekook & Devi, S. Aicevarya & Felix, Augustin & Narayanamoorthy, Samayan & Kalaiselvan, Samayan & Balaenu, Dumitru & Ahmadian, Ali, 2022. "Intuitionistic fuzzy MAUT-BW Delphi method for medication service robot selection during COVID-19," Operations Research Perspectives, Elsevier, vol. 9(C).
    14. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.
    15. Farman, Muhammad & Sarwar, Rabia & Akgul, Ali, 2023. "Modeling and analysis of sustainable approach for dynamics of infections in plant virus with fractal fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    16. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    17. Asamoah, Joshua Kiddy K. & Fatmawati,, 2023. "A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    18. Christopher Nicholas Angstmann & Byron Alexander Jacobs & Bruce Ian Henry & Zhuang Xu, 2020. "Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    19. Sajjad, Assad & Farman, Muhammad & Hasan, Ali & Nisar, Kottakkaran Sooppy, 2023. "Transmission dynamics of fractional order yellow virus in red chili plants with the Caputo–Fabrizio operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 347-368.
    20. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(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:13:p:2224-:d:847628. 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.