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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
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    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

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    Cited by:

    1. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. 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.
    3. 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.
    4. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    5. 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.

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