Analytical approach to study a mathematical model of CD4+T-cells

Abstract

Human immunodeficiency virus (HIV) emerged as one of the most serious health issues of the modern era. Till date, it challenges the scientists working in the fields related to its prevention, least spread and eradication. It affects not only the person suffering from it but also the communities and their economies. Mathematical modeling is one of the ways to explore the possibilities of prediction (and control) strategies for contagious deceases. In this paper, we have tried to extend the scope of a currently available prediction model for a continuous time span. For this purpose, an analytical investigation of the system of nonlinear differential equations, governing the HIV infection of CD4[Formula: see text]T-cells, is carried out. A new emerging analytical technique Optimal Variational Iteration Method (OVIM) has been used to obtain an analytical and convergent solution. Analytical solutions are continuous solutions that can be used to predict the phenomena without the involvement of interpolation or extrapolation errors. On the other hand, their use in the derived equations, depending upon solution itself, is far easier than the numerical solutions. We have presented the error analysis and the prediction curves graphically. Moreover, a comparison with traditional Variational Iteration is also provided. It is concluded that the traditional method fails to converge for the updated models which involve the delayed differential equations.