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

Mohamed M. Mousa and Fahad Alsharari
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Mohamed M. Mousa: Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Fahad Alsharari: Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia

Mathematics, 2021, vol. 9, issue 22, 1-12

Abstract: 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.

Keywords: SIR model; fractional derivatives; Grünwald–Letnikov method; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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