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.
Highlights
The recent trend in research has delved into mathematical modelling of real-life cases, and problems existing in the field of biological sciences have not been left out
The effect of the human immunodeficiency virus (HIV) on CD4+T cells is that it depletes and infects these cells, most important to the production of acquired immunodeficiency syndrome (AIDS). This development from HIV to AIDS happens due to the inability of human body to defend itself against other infections as the CD4+T cells are destroyed in the blood
The block methods will be adopted to solve the dynamic model that deals with the HIV infection of CD4+T cells as defined in Equation (1)
Summary
The recent trend in research has delved into mathematical modelling of real-life cases, and problems existing in the field of biological sciences have not been left out. One of the major issues which are still being investigated intensely is the human immunodeficiency virus (HIV). The effect of the HIV on CD4+T cells is that it depletes and infects these cells, most important to the production of acquired immunodeficiency syndrome (AIDS). This development from HIV to AIDS happens due to the inability of human body to defend itself against other infections as the CD4+T cells are destroyed in the blood. If the virus is detected on time and treated, the human immune system can still be protected and controlling the spread or growth of the HIV by determining which CD4+T cells are infected, and which are not [2]
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