Dynamics of fractional order delay model of coronavirus disease

Lei Zhang; Mati Ur Rahman; Shabir Ahmad; Muhammad Bilal Riaz; Fahd Jarad; Lei Zhang; Mati Ur Rahman; Shabir Ahmad; Muhammad Bilal Riaz; Fahd Jarad

doi:10.3934/math.2022234

AIMS Mathematics

2022, Volume 7, Issue 3: 4211-4232. doi: 10.3934/math.2022234

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Dynamics of fractional order delay model of coronavirus disease

1.
Department of Mathematics, Hanshan Normal University, Chaozhou, 521041, China
2.
Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road Shanghai, China
3.
Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, Pakistan
4.
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90924, Lodz, Poland
5.
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
6.
Department of Mathematics, Cankaya University, Etimesgut 06790, Ankara, Turkey
7.
King Abdulaziz University Jeddah, Saudia Arabia
8.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 19 September 2021 Revised: 05 December 2021 Accepted: 09 December 2021 Published: 17 December 2021
MSC : 92B05, 92C10, 92C15

The majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.
- fractional derivative,
- coronavirus,
- delay model,
- Adams-Bashforth method
Citation: Lei Zhang, Mati Ur Rahman, Shabir Ahmad, Muhammad Bilal Riaz, Fahd Jarad. Dynamics of fractional order delay model of coronavirus disease[J]. AIMS Mathematics, 2022, 7(3): 4211-4232. doi: 10.3934/math.2022234

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Abstract

The majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.

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