Numerical approximation of the typhoid disease model via Genocchi wavelet collocation method

Abstract

In this paper, we have considered the fractional typhoid disease model and obtained the numerical approximation of the model via the innovative wavelet scheme called the Genocchi wavelet collocation method (GWCM) with the help of Caputo fractional derivative for the fractional order. The approach under consideration is a powerful tool for obtaining numerical solutions to fractional-order nonlinear differential equations. The GWCM approach yields accurate solutions that are very close to exact solutions for highly nonlinear problems by avoiding data rounding and just computing a few terms. The Genocchi wavelet basis functions possess remarkable properties, including compact support, making them well-suited for approximating solutions to differential equations. The main benefit of this method lies in its capability to reduce the computational complexity associated with solving systems of ODEs, resulting in accurate and efficient solutions. The results of the developed technique, the RK4 method, and the ND solver have been compared. The numerical outcomes demonstrate that the implemented technique is incredibly effective and precise for solving the Typhoid model of fractional order. This paper contributes to numerical analysis by introducing the Genocchi wavelet method as a robust tool for solving biological models.