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On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative

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  • Ahmad, Shabir
  • Ullah, Aman
  • Arfan, Muhammad
  • Shah, Kamal

Abstract

In this article, the fractional-order model of the rotavirus epidemic with the effect of breastfeeding and vaccination under the Atangana-Baleanu derivative is investigated. To show the existence and uniqueness of the model fixed point theorems of Krasnoselskii and Banach are used. The Ulam-Hyres stability is carried out for the proposed model by using the notion of non-linear functional analysis. The numerical scheme is determined for finding the approximate solution of the proposed model by using the fractional Adams-Bashforth method. Numerical simulations are provided for different fractional order to give the transmission dynamics of the rotavirus epidemic.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306299
    DOI: 10.1016/j.chaos.2020.110233
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    References listed on IDEAS

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    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Awawdeh, Fadi & Adawi, A. & Mustafa, Z., 2009. "Solutions of the SIR models of epidemics using HAM," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3047-3052.
    4. 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.
    5. 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.
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    Cited by:

    1. Rubayyi T. Alqahtani & Shabir Ahmad & Ali Akgül, 2021. "Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense," Mathematics, MDPI, vol. 9(19), pages 1-21, September.
    2. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. 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.
    4. Rubayyi T. Alqahtani & Shabir Ahmad & Ali Akgül, 2021. "Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense," Mathematics, MDPI, vol. 9(21), pages 1-21, November.
    5. Ndenda, J.P. & Njagarah, J.B.H. & Shaw, S., 2021. "Role of immunotherapy in tumor-immune interaction: Perspectives from fractional-order modelling and sensitivity analysis," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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