A chaos study of fractional SIR epidemic model of childhood diseases

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 arbitrary-order 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.

Keywords

• SIR epidemic model
• Laguerre wavelets
• Operational matrix
• Fractional-order differential equations (FDEs)
• Fractional derivatives
• Dynamical systems