A chaos study of fractional SIR epidemic model of childhood diseases
Date
2021
Authors
Momani, Shaher
Kumar, Ranbir
Srivastava, H.M.
Kumar, Sunil
Hadid, Samir
Journal Title
Journal ISSN
Volume Title
Publisher
Results in Physics
Abstract
Models of bio-mathematics are experimental systems that recreate aspects of human tissue function, diseases or
virus. In this research, a new operational matrix based on the Laguerre wavelets is introduced for a arbitraryorder
susceptible-infected-recovered (SIR) epidemic dynamical system of childhood diseases. An exact mechanism
for the Riemann–Liouville arbitrary integral operator for the Laguerre wavelets is explained where the
arbitrary-order derivative is assumed in the Liouville-Caputo style. Further, we use this operational matrix to
convert the given dispute into a system of algebraic equations. The chaotic attractors for fractional-order SIR
dynamical model are illustrated graphically by adopting the Adams–Bashforth-Moulton (ABM) scheme. Numerical
simulations and results for the susceptible, infected and recovered peoples are carried out by using the
Laguerre wavelets. Their behaviour with respect to time is seen to be the key features of this work. Moreover, we
have compared the Laguerre wavelet solutions with the ABM solution for the truthfulness and applicability of the
Laguerre wavelets scheme.
Description
Keywords
SIR epidemic model, Laguerre wavelets, Operational matrix, Fractional-order differential equations (FDEs), Fractional derivatives, Dynamical systems, Adams-Bashforth-Moulton method
Citation
Momani, S., Kumar, R., Srivastava, H. M., Kumar, S., & Hadid, S. (2021). A chaos study of fractional SIR epidemic model of childhood diseases. Results in Physics, 27, 1-17. https://doi.org/10.1016/j.rinp.2021.104422.