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SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels

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  • Jena, Rajarama Mohan
  • Chakraverty, Snehashish
  • Baleanu, Dumitru

Abstract

Vaccination programs for infants have significantly affected childhood morbidity and mortality. The primary goal of health administrators is to protect children against diseases that can be prevented by vaccination. In this manuscript, we have applied the homotopy perturbation Elzaki transform method to obtain the solutions of the epidemic model of childhood diseases involving time-fractional order Atangana–Baleanu and Caputo–Fabrizio derivatives. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. Although Elzaki transform is an effective method for solving fractional differential equations, this method sometimes fails to handle nonlinear terms from the fractional differential equations. These difficulties may be overcome by coupling this transform with that of HPM. This method offers a rapidly convergent series solutions. Validation and usefulness of the technique are incorporated with new fractional-order derivatives with exponential decay law and with general Mittag-Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo, Atangana–Baleanu, and Caputo–Fabrizio derivatives is discussed.

Suggested Citation

  • Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2021. "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 514-534.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:514-534
    DOI: 10.1016/j.matcom.2020.11.017
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    References listed on IDEAS

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    1. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.
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    5. Jena, Rajarama Mohan & Chakraverty, Snehashish & Jena, Subrat Kumar, 2020. "Analysis of the dynamics of phytoplankton nutrient and whooping cough models with nonsingular kernel arising in the biological system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    3. Turkyilmazoglu, Mustafa, 2022. "A restricted epidemic SIR model with elementary solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
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    5. Vivekanandhan, Gayathri & Nourian Zavareh, Mahdi & Natiq, Hayder & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Svetec, Milan, 2022. "Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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