Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators

Nadiyah Hussain Alharthi; Mdi Begum Jeelani; Nadiyah Hussain Alharthi; Mdi Begum Jeelani

doi:10.3934/math.20231382

AIMS Mathematics

2023, Volume 8, Issue 11: 27009-27032. doi: 10.3934/math.20231382

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Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators

Department of mathematics and statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

Received: 23 June 2023 Revised: 17 August 2023 Accepted: 30 August 2023 Published: 22 September 2023
MSC : 34A08, 47H08, 93A30

Recently, the area devoted to mathematical epidemiology has attracted much attention. Mathematical formulations have served as models for various infectious diseases. In this regard, mathematical models have also been used to study COVID-19, a threatening disease in present time. This research work is devoted to consider a SEIR (susceptible-exposed-infectious-removed) type mathematical model for investigating COVID-19 alongside a new scenario of fractional calculus. We consider piece-wise fractional order derivatives to investigate the proposed model for qualitative and computational analysis. The results related to the qualitative analysis are studied via using the tools of fixed point approach. In addition, the computational analysis is performed due to a significance of simulation to understand the transmission dynamics of COVID-19 infection in the community. In addition, a numerical scheme based on Newton's polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Additionally, some real data results are also shown in comparison to the numerical results.
- dynamical system,
- piecewise derivative,
- Newton polynomials,
- fractional order iterative method
Citation: Nadiyah Hussain Alharthi, Mdi Begum Jeelani. Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators[J]. AIMS Mathematics, 2023, 8(11): 27009-27032. doi: 10.3934/math.20231382

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Abstract

Recently, the area devoted to mathematical epidemiology has attracted much attention. Mathematical formulations have served as models for various infectious diseases. In this regard, mathematical models have also been used to study COVID-19, a threatening disease in present time. This research work is devoted to consider a SEIR (susceptible-exposed-infectious-removed) type mathematical model for investigating COVID-19 alongside a new scenario of fractional calculus. We consider piece-wise fractional order derivatives to investigate the proposed model for qualitative and computational analysis. The results related to the qualitative analysis are studied via using the tools of fixed point approach. In addition, the computational analysis is performed due to a significance of simulation to understand the transmission dynamics of COVID-19 infection in the community. In addition, a numerical scheme based on Newton's polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Additionally, some real data results are also shown in comparison to the numerical results.

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