Study of the biological behavior of Tuberculosis and Dengue Disease model via Hermite wavelets based a new numerical method
Vivek

Applied Sciences and Humanities Department, Institute of Engineering and Technology, Lucknow, Uttar Pradesh India 243723.

Abstract

This study presents the application of a wavelet-based approach to solve two mathematical models. The first model deals with the spread of Dengue disease, considering various factors such as transmission rate and death rate. The second model focuses on the spread of Tuberculosis, incorporating different control parameters. To solve these systems of nonlinear differential equations, we employ the Hermite wavelet collocation method (HWCM), which utilizes the operational matrix of integration of Hermite wavelets. This method transforms the original nonlinear differential equations into solvable algebraic equations. Subsequently, the numerical solution is obtained using the Newton-Raphson method. We compare the outcomes of the proposed method with analytical solutions, solutions obtained using Bernoulli wavelets, and the Runge-Kutta method. Additionally, we discuss several theorems to analyze the convergence of the proposed method. Our results demonstrate that the proposed method achieves superior accuracy and reduced error compared to existing methods.

Keywords: Tuberculosis and Dengue Disease Model, Hermite Wavelet, Collocation Technique, MATLAB

Topic: Minisymposia Differential Equations