Mathematics and Statistics Vol. 9(3), pp. 371 - 378
DOI: 10.13189/ms.2021.090319
Reprint (PDF) (787Kb)

Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model

Adeyeye Oluwaseun ^*, Omar Zurni
Department of Mathematics & Statistics, School of Quantitative Sciences, Malaysia

ABSTRACT

Some of the issues relating to the human immunodeficiency virus (HIV) epidemic can be expressed as a system of nonlinear first order ordinary differential equations. This includes modelling the spread of the HIV virus in infecting CD4+T cells that help the human immune system to fight diseases. However, real life differential equation models usually fail to have an exact solution, which is also the case with the nonlinear model considered in this article. Thus, an approximate method, known as the block method, is developed to solve the system of first order nonlinear differential equation. To develop the block method, a linear block approach was adopted, and the basic properties required to classify the method as convergent were investigated. The block method was found to be convergent, which ascertained its usability for the solution of the model. The solution obtained from the newly developed method in this article was compared to previous methods that have been adopted to solve same model. In order to have a justifiable basis of comparison, two-step length values were substituted to obtain a one-step and two-step block method. The results show the newly developed block method obtaining accurate results in comparison to previous studies. Hence, this article has introduced a new method suitable for the direct solution of first order differential equation models without the need to simplify to a system of linear algebraic equations. Likewise, its convergent properties and accuracy also give the block method an edge over existing methods.

KEYWORDS
HIV Infection, CD4+T Cells, Numerical, Block Method, First Order

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Adeyeye Oluwaseun , Omar Zurni , "Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model," Mathematics and Statistics, Vol. 9, No. 3, pp. 371 - 378, 2021. DOI: 10.13189/ms.2021.090319.

(b). APA Format:
Adeyeye Oluwaseun , Omar Zurni (2021). Block Method for the Solution of First Order Nonlinear ODEs and Its Application to HIV Infection of CD4+T Cells Model. Mathematics and Statistics, 9(3), 371 - 378. DOI: 10.13189/ms.2021.090319.