Communicable disease model in view of fractional calculus

Weam G. Alharbi; Abdullah F. Shater; Abdelhalim Ebaid; Carlo Cattani; Mounirah Areshi; Mohammed M. Jalal; Mohammed K. Alharbi; Weam G. Alharbi; Abdullah F. Shater; Abdelhalim Ebaid; Carlo Cattani; Mounirah Areshi; Mohammed M. Jalal; Mohammed K. Alharbi

doi:10.3934/math.2023508

AIMS Mathematics

2023, Volume 8, Issue 5: 10033-10048. doi: 10.3934/math.2023508

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Research article

Communicable disease model in view of fractional calculus

1.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
2.
Department of Medical Laboratory Technology, Faculty of Applied Medical Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia
3.
Engineering School (DEIM), University of Tuscia, Viterbo, Italy
4.
Department of Physical Therapy, Faculty of Applied Medical Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia

Received: 10 January 2023 Revised: 15 February 2023 Accepted: 19 February 2023 Published: 24 February 2023
MSC : 34A08

The COVID-19 pandemic still gains the attention of many researchers worldwide. Over the past few months, China faced a new wave of this pandemic which increases the risk of its spread to the rest of the world. Therefore, there has become an urgent demand to know the expected behavior of this pandemic in the coming period. In this regard, there are many mathematical models from which we may obtain accurate predictions about the behavior of this pandemic. Such a target may be achieved via updating the mathematical models taking into account the memory effect in the fractional calculus. This paper generalizes the power-law growth model of the COVID-19. The generalized model is investigated using two different definitions in the fractional calculus, mainly, the Caputo fractional derivative and the conformable derivative. The solution of the first-model is determined in a closed series form and the convergence is addressed. At a specific condition, the series transforms to an exact form. In addition, the solution of the second-model is evaluated exactly. The results are applied on eight European countries to predict the behavior/variation of the infected cases. Moreover, some remarks are given about the validity of the results reported in the literature.
- fractional differential equation,
- conformable,
- initial value problem,
- series solution,
- exact solution
Citation: Weam G. Alharbi, Abdullah F. Shater, Abdelhalim Ebaid, Carlo Cattani, Mounirah Areshi, Mohammed M. Jalal, Mohammed K. Alharbi. Communicable disease model in view of fractional calculus[J]. AIMS Mathematics, 2023, 8(5): 10033-10048. doi: 10.3934/math.2023508

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Abstract

The COVID-19 pandemic still gains the attention of many researchers worldwide. Over the past few months, China faced a new wave of this pandemic which increases the risk of its spread to the rest of the world. Therefore, there has become an urgent demand to know the expected behavior of this pandemic in the coming period. In this regard, there are many mathematical models from which we may obtain accurate predictions about the behavior of this pandemic. Such a target may be achieved via updating the mathematical models taking into account the memory effect in the fractional calculus. This paper generalizes the power-law growth model of the COVID-19. The generalized model is investigated using two different definitions in the fractional calculus, mainly, the Caputo fractional derivative and the conformable derivative. The solution of the first-model is determined in a closed series form and the convergence is addressed. At a specific condition, the series transforms to an exact form. In addition, the solution of the second-model is evaluated exactly. The results are applied on eight European countries to predict the behavior/variation of the infected cases. Moreover, some remarks are given about the validity of the results reported in the literature.

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