On a SEIR-type model of COVID-19 using piecewise and stochastic differential operators undertaking management strategies

Mdi Begum Jeelani; Kamal Shah; Hussam Alrabaiah; Abeer S. Alnahdi; Mdi Begum Jeelani; Kamal Shah; Hussam Alrabaiah; Abeer S. Alnahdi

doi:10.3934/math.20231395

AIMS Mathematics

2023, Volume 8, Issue 11: 27268-27290. doi: 10.3934/math.20231395

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On a SEIR-type model of COVID-19 using piecewise and stochastic differential operators undertaking management strategies

1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
2.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
3.
Department of Computer Science and Mathematics, Lebanese American University, Byblos Lebanon
4.
College of Engineering, Al Ain University, Al Ain, UAE
5.
Department of Mathematics, Tafila Technical University, Tafila, Jordan

Received: 03 August 2023 Revised: 23 August 2023 Accepted: 28 August 2023 Published: 26 September 2023
MSC : 03C65, 26A33, 34A08

In this work, an epidemic model of a susceptible, exposed, infected and recovered SEIR-type is established for the distinctive dynamic compartments and epidemic characteristics of COVID-19 as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractional calculus known as piecewise derivatives. The existence theory is demonstrated through the establishment of sufficient conditions. In addition, result related to Hyers-Ulam stability is also derived for the considered model. A numerical method based on modified Euler procedure is also constructed to simulate the approximate solutions of the proposed model by employing various values of fractional orders. We testified the numerical results by using real available data of Japan. In addition, some results for the SEIR-type model are also presented graphically using the stochastic process, and the obtained results are discussed.
- SEIR system,
- piecewise derivative,
- stochastic derivative,
- numerical scheme,
- existence theory
Citation: Mdi Begum Jeelani, Kamal Shah, Hussam Alrabaiah, Abeer S. Alnahdi. On a SEIR-type model of COVID-19 using piecewise and stochastic differential operators undertaking management strategies[J]. AIMS Mathematics, 2023, 8(11): 27268-27290. doi: 10.3934/math.20231395

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Abstract

In this work, an epidemic model of a susceptible, exposed, infected and recovered SEIR-type is established for the distinctive dynamic compartments and epidemic characteristics of COVID-19 as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractional calculus known as piecewise derivatives. The existence theory is demonstrated through the establishment of sufficient conditions. In addition, result related to Hyers-Ulam stability is also derived for the considered model. A numerical method based on modified Euler procedure is also constructed to simulate the approximate solutions of the proposed model by employing various values of fractional orders. We testified the numerical results by using real available data of Japan. In addition, some results for the SEIR-type model are also presented graphically using the stochastic process, and the obtained results are discussed.

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