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

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  • 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
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    References listed on IDEAS

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    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.
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    1. 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).
    2. 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).
    3. 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).
    4. 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).
    5. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. 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).
    7. 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).
    8. 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).
    9. 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).
    10. 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).
    11. 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).
    12. 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).
    13. Hincal, Evren & Alsaadi, Sultan Hamed, 2021. "Stability analysis of fractional order model on corona transmission dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    14. 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).
    15. 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).
    16. 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).
    17. 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).
    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).

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