On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel

Saima Rashid; Fahd Jarad; Fatimah S. Bayones; Saima Rashid; Fahd Jarad; Fatimah S. Bayones

doi:10.3934/math.2022254

AIMS Mathematics

2022, Volume 7, Issue 3: 4552-4573. doi: 10.3934/math.2022254

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On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 14 November 2021 Revised: 12 December 2021 Accepted: 16 December 2021 Published: 23 December 2021
MSC : 46S40, 47H10, 54H25

The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.
- Elzaki transform,
- ABC fractional derivative operator,
- childhood diseases model,
- fixed point theory,
- Picard–Lindelöf method
Citation: Saima Rashid, Fahd Jarad, Fatimah S. Bayones. On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel[J]. AIMS Mathematics, 2022, 7(3): 4552-4573. doi: 10.3934/math.2022254

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Abstract

The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.

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