Open Access

ARTICLE

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

by Fei Li¹, Haci Mehmet Baskonus^2,*, S. Kumbinarasaiah³, G. Manohara³, Wei Gao⁴, Esin Ilhan⁵

1 Department of Scientific Research, Yunnan Normal University, Kunming, 650500, China
2 Department of Mathematics and Science Education, Harran University, Sanliurfa, 63050, Türkiye
3 Department of Mathematics, Bangalore University, Bengaluru, 560056, India
4 School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, China
5 Faculty of Engineering and Architecture, Kirsehir Ahi Evran University, Kırsehir, 40500, Türkiye

* Corresponding Author: Haci Mehmet Baskonus. Email:

(This article belongs to the Special Issue: Recent Developments on Computational Biology-I)

Computer Modeling in Engineering & Sciences 2023, 137(3), 2381-2408. https://doi.org/10.32604/cmes.2023.028069

Received 28 November 2022; Accepted 17 March 2023; Issue published 03 August 2023

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.

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Keywords

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