IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v135y2020ics0960077920302678.html
   My bibliography  Save this article

On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative

Author

Listed:
  • Abdo, Mohammed S.
  • Shah, Kamal
  • Wahash, Hanan A.
  • Panchal, Satish K.

Abstract

The major purpose of the presented study is to analyze and find the solution for the model of nonlinear fractional differential equations (FDEs) describing the deadly and most parlous virus so-called coronavirus (COVID-19). The mathematical model depending of fourteen nonlinear FDEs is presented and the corresponding numerical results are studied by applying the fractional Adams Bashforth (AB) method. Moreover, a recently introduced fractional nonlocal operator known as Atangana-Baleanu (AB) is applied in order to realize more effectively. For the current results, the fixed point theorems of Krasnoselskii and Banach are hired to present the existence, uniqueness as well as stability of the model. For numerical simulations, the behavior of the approximate solution is presented in terms of graphs through various fractional orders. Finally, a brief discussion on conclusion about the simulation is given to describe how the transmission dynamics of infection take place in society.

Suggested Citation

  • Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    • Handle: RePEc:eee:chsofr:v:135:y:2020:i:c:s0960077920302678
    DOI: 10.1016/j.chaos.2020.109867
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920302678
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109867?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. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    3. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    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. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Kucche, Kishor D. & Sutar, Sagar T., 2021. "Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Hincal, Evren & Alsaadi, Sultan Hamed, 2021. "Stability analysis of fractional order model on corona transmission dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Ahmad, Shabir & Ullah, Aman & Al-Mdallal, Qasem M. & Khan, Hasib & Shah, Kamal & Khan, Aziz, 2020. "Fractional order mathematical modeling of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Erturk, Vedat Suat & Kumar, Pushpendra, 2020. "Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Abdo, Mohammed S. & Abdeljawad, Thabet & Ali, Saeed M. & Shah, Kamal & Jarad, Fahd, 2020. "Existence of positive solutions for weighted fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Batistela, Cristiane M. & Correa, Diego P.F. & Bueno, Átila M & Piqueira, José Roberto C., 2021. "SIRSi compartmental model for COVID-19 pandemic with immunity loss," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    10. Silva, Petrônio C.L. & Batista, Paulo V.C. & Lima, Hélder S. & Alves, Marcos A. & Guimarães, Frederico G. & Silva, Rodrigo C.P., 2020. "COVID-ABS: An agent-based model of COVID-19 epidemic to simulate health and economic effects of social distancing interventions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Rehman, Attiq ul & Singh, Ram & Agarwal, Praveen, 2021. "Modeling, analysis and prediction of new variants of covid-19 and dengue co-infection on complex network," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    12. 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).
    13. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    14. Baba, Isa Abdullahi & Rihan, Fathalla A. & Hincal, Evren, 2023. "A fractional order model that studies terrorism and corruption codynamics as epidemic disease," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    15. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    16. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. Crokidakis, Nuno, 2020. "COVID-19 spreading in Rio de Janeiro, Brazil: Do the policies of social isolation really work?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    18. Sutar, Sagar T. & Kucche, Kishor D., 2021. "On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    19. Malki, Zohair & Atlam, El-Sayed & Hassanien, Aboul Ella & Dagnew, Guesh & Elhosseini, Mostafa A. & Gad, Ibrahim, 2020. "Association between weather data and COVID-19 pandemic predicting mortality rate: Machine learning approaches," Chaos, Solitons & Fractals, Elsevier, vol. 138(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. Mahmood, Tariq & ur Rahman, Mati & Arfan, Muhammad & Kayani, Sadaf-Ilyas & Sun, Mei, 2023. "Mathematical study of Algae as a bio-fertilizer using fractal–fractional dynamic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 207-222.
    2. Suwan, Iyad & Abdeljawad, Thabet & Jarad, Fahd, 2018. "Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 50-59.
    3. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    4. Chatibi, Y. & El Kinani, E.H. & Ouhadan, A., 2019. "Variational calculus involving nonlocal fractional derivative with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 117-121.
    5. Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    6. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    7. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    8. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    10. Kubeka, Amos S. & Doungmo Goufo, Emile F. & Khumalo, Melusi, 2018. "On the quasi-normal modes of a Schwarzschild white hole for the lower angular momentum and perturbation by non-local fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 348-357.
    11. Ghanbari, Behzad & Gómez-Aguilar, J.F., 2018. "Modeling the dynamics of nutrient–phytoplankton–zooplankton system with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 114-120.
    12. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    13. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    14. Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    15. Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
    16. Atangana, Ernestine, 2019. "New insight kinetic modeling: Models above classical chemical mechanic," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 16-24.
    17. Alzahrani, E.O. & Khan, M.A., 2018. "Modeling the dynamics of Hepatitis E with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 287-301.
    18. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Saad, Khaled M. & Khan, Muhammad Altaf & Agarwal, P., 2019. "Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 48-65.
    19. Owolabi, Kolade M. & Karaagac, Berat, 2020. "Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    20. Avcı, Derya & Yetim, Aylin, 2019. "Cauchy and source problems for an advection-diffusion equation with Atangana–Baleanu derivative on the real line," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 361-365.

    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:135:y:2020:i:c:s0960077920302678. 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.