A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases

The objective of this work is to examine the dynamics of a fractional-order susceptible-infectious-recovered (SIR) model that simulate epidemiological diseases such as childhood diseases. An effective numerical scheme based on Grünwald–Letnikov fractional derivative is suggested to solve the conside...

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Autores principales:	Mohamed M. Mousa, Fahad Alsharari
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	SIR model fractional derivatives Grünwald–Letnikov method stability analysis Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0a77e173381940b0801a1cc772131d99
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spelling	oai:doaj.org-article:0a77e173381940b0801a1cc772131d992021-11-25T18:16:29ZA Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases10.3390/math92228472227-7390https://doaj.org/article/0a77e173381940b0801a1cc772131d992021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2847https://doaj.org/toc/2227-7390The objective of this work is to examine the dynamics of a fractional-order susceptible-infectious-recovered (SIR) model that simulate epidemiological diseases such as childhood diseases. An effective numerical scheme based on Grünwald–Letnikov fractional derivative is suggested to solve the considered model. A stability analysis is performed to qualitatively examine the dynamics of the SIR model. The reliability and robustness of the proposed scheme is demonstrated by comparing obtained results with results obtained from a fourth order Runge–Kutta built-in Maple syntax when considering derivatives of integer order. Graphical illustrations of the numerical results are given. The inaccuracy of some results presented in two studies exist in the literature have been clearly explained. Generalizing of the cases examined in another study, by considering a model with fraction-order derivatives, is another objective of this work as well.Mohamed M. MousaFahad AlsharariMDPI AGarticleSIR modelfractional derivativesGrünwald–Letnikov methodstability analysisMathematicsQA1-939ENMathematics, Vol 9, Iss 2847, p 2847 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	SIR model fractional derivatives Grünwald–Letnikov method stability analysis Mathematics QA1-939
spellingShingle	SIR model fractional derivatives Grünwald–Letnikov method stability analysis Mathematics QA1-939 Mohamed M. Mousa Fahad Alsharari A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases
description	The objective of this work is to examine the dynamics of a fractional-order susceptible-infectious-recovered (SIR) model that simulate epidemiological diseases such as childhood diseases. An effective numerical scheme based on Grünwald–Letnikov fractional derivative is suggested to solve the considered model. A stability analysis is performed to qualitatively examine the dynamics of the SIR model. The reliability and robustness of the proposed scheme is demonstrated by comparing obtained results with results obtained from a fourth order Runge–Kutta built-in Maple syntax when considering derivatives of integer order. Graphical illustrations of the numerical results are given. The inaccuracy of some results presented in two studies exist in the literature have been clearly explained. Generalizing of the cases examined in another study, by considering a model with fraction-order derivatives, is another objective of this work as well.
format	article
author	Mohamed M. Mousa Fahad Alsharari
author_facet	Mohamed M. Mousa Fahad Alsharari
author_sort	Mohamed M. Mousa
title	A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases
title_short	A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases
title_full	A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases
title_fullStr	A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases
title_full_unstemmed	A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases
title_sort	comparative numerical study and stability analysis for a fractional-order sir model of childhood diseases
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0a77e173381940b0801a1cc772131d99
work_keys_str_mv	AT mohamedmmousa acomparativenumericalstudyandstabilityanalysisforafractionalordersirmodelofchildhooddiseases AT fahadalsharari acomparativenumericalstudyandstabilityanalysisforafractionalordersirmodelofchildhooddiseases AT mohamedmmousa comparativenumericalstudyandstabilityanalysisforafractionalordersirmodelofchildhooddiseases AT fahadalsharari comparativenumericalstudyandstabilityanalysisforafractionalordersirmodelofchildhooddiseases
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A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases

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