An Efficient Numerical Scheme for Biological Models in the Frame of Bernoulli Wavelets

Abstract

This article considers three types of biological systems: the dengue fever disease model, the COVID-19 virus model, and the transmission of Tuberculosis model. The new technique of creating the integration matrix for the Bernoulli wavelets is applied. Also, the novel method proposed in this paper is called the Bernoulli wavelet collocation scheme (BWCM). All three models are in the form system of coupled ordinary differential equations without an exact solution. These systems are converted into a system of algebraic equations using the Bernoulli wavelet collocation scheme. The numerical wave distributions of these governing models are obtained by solving the algebraic equations via the Newton-Raphson method. The results obtained from the developed strategy are compared to several schemes such as the Runge Kutta method, and ND solver in mathematical software. The convergence analyses are discussed through theorems. The newly implemented Bernoulli wavelet method improves the accuracy and converges when it is compared with the existing methods in the literature.