Eur. Phys. J. Plus (2019) 134: 265
https://doi.org/10.1140/epjp/i2019-12599-8

Regular Article

A mathematical model on HIV/AIDS with fusion effect: Analysis and homotopy solution

Department of Mathematics, National Institute of Technology, 788010, Silchar, Assam, India

^* e-mail: pkguptaitbhu@gmail.com

Received: 20 October 2018
Accepted: 28 February 2019
Published online: 17 June 2019

Abstract

In this study, first we analyzed the dynamical behaviour of a deterministic dynamic model for HIV-infected CD4⁺ T cells in a population of three classes of cell compartments: uninfected, infected and virus, with fusion effect. The qualitative analysis of the model, i.e., positivity and boundedness of the solutions have been discussed. For the proposed model, the non-infected and endemic equilibrium points are recognized and their local stability examined by the Jacobian matrix. The Lyapunov functional and geometric approaches are discussed in detail in order to show the global stability of the non-infected and endemic equilibrium states, respectively. Additional to this qualitative analysis, the approximate analytical solution was obtained for the proposed model with the help of the homotopy analysis method (HAM), and we demonstrated the convergence region by the ℏ curve. The residual error is also calculated for the HAM solution. We have drawn the numerical solutions to confirm all analytical and HAM solution, which reflects the reliability of all solutions.