Efficient Numerical Scheme for the Solution of HIV Infection CD4+ T-Cells Using Haar Wavelet Technique

Rohul Amin,Shah Nazir,Şuayip Yüzbası

doi:10.32604/cmes.2022.019154

Rohul Amin, Shah Nazir + Show 1 more

Open Access

https://doi.org/10.32604/cmes.2022.019154

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Abstract

In this paper, Haar collocation algorithm is developed for the solution of first-order of HIV infection CD4+ T-Cells model. In this technique, the derivative in the nonlinear model is approximated by utilizing Haar functions. The value of the unknown function is obtained by the process of integration. Error estimation is also discussed, which aims to reduce the error of numerical solutions. The numerical results show that the method is simply applicable. The results are compared with Runge-Kutta technique, Bessel collocation technique, LADM-Pade and Galerkin technique available in the literature. The results show that the Haar technique is easy, precise and effective.

Highlights

Many models have been developed by mathematicians in the last decade to explain the immunological response to Human Immunodeficiency Virus (HIV) infection
Due to the scarcity of CD4+ T-cells, HIV disease is considered to result in concealment of the immune system, cells which play a focal part in the human immune system
6 Conclusion Haar collocation scheme is developed for the solution of the HIV CD4+ T-cells model

Summary

Introduction

Many models have been developed by mathematicians in the last decade to explain the immunological response to Human Immunodeficiency Virus (HIV) infection. Khater et al [20] developed a semi analytical and numerical scheme for a biological model. Khater et al [23] used trigonometric Quintic B-spline method for the solution of conformable fractional nonlinear time-space telegraph equation. Khater et al [26] investigated the analytical and semi-analytical solutions of the time-fractional Cahn–Allen equation by using the Adomian decomposition method. Khater et al [27] found the analytical solutions of the nonlinear Schrodinger equation with the higher-order through Kudryashov method. Khater et al [29] used the trigonometric quintic and exponential cubic B-spline schemes for the solutions of the nonlinear Klein-Gordon-Zakharov model. We develop an accurate scheme by using HWC technique for the solution of the HIV infection of CD4+ T-cells. To develop efficient numerical scheme by utilizing HWC technique for HIV infection CD4+ T-cells.

Haar Wavelet

Numerical Method

Error Estimation

Numerical Applications

Conclusion