IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i3p555-d1042475.html
   My bibliography  Save this article

A New Incommensurate Fractional-Order COVID 19: Modelling and Dynamical Analysis

Author

Listed:
  • Abdallah Al-Husban

    (Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan)

  • Noureddine Djenina

    (Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Rania Saadeh

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • Adel Ouannas

    (Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Giuseppe Grassi

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

Abstract

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the S E I R model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:555-:d:1042475
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/3/555/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/3/555/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Diaz, Paul & Constantine, Paul & Kalmbach, Kelsey & Jones, Eric & Pankavich, Stephen, 2018. "A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 141-155.
    2. 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.
    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. Wang, Jinling & Jiang, Haijun & Ma, Tianlong & Hu, Cheng, 2019. "Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 148-157.
    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. Dun, Han & Shuting, Yan & She, Han & Lingfei, Qian & Chris, Ampimah Benjamin, 2019. "Research on how the difference of personal propagation ability influences the epidemic spreading in activity-driven network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 311-318.
    4. Liu, Liya & Jiang, Daqing & Hayat, Tasawar, 2021. "Dynamics of an SIR epidemic model with varying population sizes and regime switching in a two patch setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    5. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Cen Song & Sijia Zhou & Kyle Hunt & Jun Zhuang, 2022. "Comprehensive Evolution Analysis of Public Perceptions Related to Pediatric Care: A Sina Weibo Case Study (2013–2020)," SAGE Open, , vol. 12(1), pages 21582440221, March.
    7. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    8. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    9. Alexandru Topîrceanu, 2023. "On the Impact of Quarantine Policies and Recurrence Rate in Epidemic Spreading Using a Spatial Agent-Based Model," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    10. Dantas, Eber & Tosin, Michel & Cunha Jr, Americo, 2018. "Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 249-259.
    11. 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.

    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:11:y:2023:i:3:p:555-:d:1042475. 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.