On dynamics of a mathematical model for HIV infection with fusion effect and cure rate

Abstract

In this manuscript, we have proposed and analyzed a differential equation model for HIV infection to study the dynamics of three different populations: HIV-free CD4⁺ T cells, HIV-infected CD4⁺ T cells and free virus of the model. In the model, we have incorporated fusion effect for HIV-free CD4⁺ T cell and free virus, proliferation of HIV-free CD4⁺ T cells which follows a full logistic growth term and cure rate for HIV-infected CD4⁺ T cells. Our main objective is to investigate the effects of fusion and cure rate on the dynamics of the model. We have used next generation matrix method to calculate the basic reproduction number (R₀) for this proposed model. Local stability of the existing equilibrium points is discussed using Routh-Hurwitz theorem. Also, in order to establish the global stability criteria Lyapunov functional and geometric approach are used. From the analysis it is found that if the basic reproduction number R₀ ≤ 1, HIV will be removed from the population of CD4⁺ T cells and if R₀ > 1, there exists chronic infection. Also, we have carried out numerical simulations in order to verify the analytic results.