A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials. Issue 2 (29th October 2020)

• Record Type: Journal Article
• Authors: Kumar, Sunil; Kumar, Ranbir; Osman, M. S.; Samet, Bessem
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 2(2021)
• Page Start: 1250
• Page End: 1268
• Publication Date: 2020-10-29
• Subjects: Adams‐Bashforth‐Moulton predictor corrector scheme -- fractional derivatives -- Genocchi wavelets -- measles model -- operational matrix; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22577
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: Epidemiology is the glorious discipline underlying medical research, public health practice, and health care evaluation. Nowadays, research on disease models with anonymous parameters is a popular issue for researchers working in epidemiology. Due to popularity of this field, a new numerical method for the solution of the fractional SEIR epidemic of measles is introduced where fractional derivative is taken in Caputo sense. We have discussed about the framework of Genocchi wavelets for numerical simulations of above disease model. Furthermore, the operational matrix merged with the collocation method is used in order to convert fractional‐order problem into algebraic equations. The Adams‐Bashforth‐Moulton (ABM) numerical scheme is used to solve above disease model with various parameters. For we have compared the solutions with Adams‐Bashforth‐Moulton predictor corrector scheme for the accuracy and applicability of the Genocchi wavelets method (GWM). The behaviors of susceptible, exposed, infected, and recovered individuals are presented graphically at the value of various fractional order. The error and convergence analysis of the Genocchi wavelets has been discussed for the applicability of the present methods. Further, various numerical simulations have been carried out to justify our achieved finding.