Solution of a System of HIV Model Equations by the Variational Iteration Method

Tormitim Terdoo Timothy¹, Aboiyar Terhemen¹, Kimbir Anande Richard¹ and Emmanuel Olumuyiwa Onifade^2,

¹Department of Mathematics/Statistics/Computer Science, University Of Agriculture, PMB 2373 Makurdi, Benue State, Nigeria

²Department of Microbiology, University of Agriculture, PMB 2373 Makurdi, Benue State, Nigeria

Cite this paper:
Tormitim Terdoo Timothy, Aboiyar Terhemen, Kimbir Anande Richard and Emmanuel Olumuyiwa Onifade. Solution of a System of HIV Model Equations by the Variational Iteration Method. American Journal of Applied Mathematics and Statistics. 2019; 7(6):205-223. doi: 10.12691/ajams-7-6-3

Abstract

Mathematical modeling of many biological systems leads to ordinary differential equations (ODEs), which are often too complicated to solve exactly. Acquire Immune Deficiency Syndrome (AIDS) is one of the greatest health challenges of this millennium and it is caused by a virus called Human Immunodeficiency Virus (HIV). This work is a nonlinear mathematical model of HIV/AIDS dynamics considering Counseling and Anti-Retroviral Therapy (ART) which was developed in the form of differential equation. Three sub-models of the general model considered were the sub-model without ART, the sub-model with only infected males receiving ART and the sub-model with only infected females receiving ART. The general model and the sub-models with various parameter values are solved using the Variational Iteration Method (VIM), which is a semi analytical method. The VIM is used to obtain solutions of both nonlinear and linear functional equations without discretizing the equations or approximating the operators. The solution when it exists is found in a rapidly converging series form. The VIM provided continuous solutions to the model which can be used for further analysis like differentiation and integration and can be used to compute prevalence rates. Solutions of the model, presented in graphical form and the results revealed that VIM is an alternative method for the fourth-order Runge Kutta method. It was also observed that for effective counseling and ART to lead eradication, it necessary that the same proportion of males and females should be involved in ART. The existence of the disease free equilibrium state of the general model is investigated and shown to be locally and asymptotically stable (LAS).

Keywords:
virus susceptible infective counseling variation eradication

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