Stability of a CD4+ T cell viral infection model with diffusion.

This paper is devoted to the study of the stability of a CD 4 + T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value ℛ 0 ≤ 1 ; the endemic equilibrium is globally asymptotically stable if ℛ 0 > 1 and d u ∗ − δ w ∗ ≥ 0. Finally, we give an application and numerical simulations to illustrate the main results. [ABSTRACT FROM AUTHOR]