Stability of a delayed HIV-1 dynamics model with Beddington-DeAngelis functional response and absorption effect with two delays

Abstract

This research examined the stability properties of a set of delay differential equations for HIV-I infection that includes a Beddington-DeAngelis functional response. The model has incorporated with two-time delays namely intracellular time delay and maturation time delay, and the absorption effect in order to make the processes more biologically sensitive. We prove that the infection free equilibrium and the chronic infection equilibrium be locally asymptotically stable if the basic reproduction number R₀ ≤ 1 and R₀ > 1 respectively, by using the characteristic equations of dynamics model and Routh Hurwitz stability criterion. It is shown that, if R₀ ≤ 1, the infection-free equilibrium is globally asymptotically stable by using appropriate Lyapunov function and LaSalle’s invariance principle. Further, we have established the conditions for the permanence of the system. In addition, numerical simulations are performed to illustrate the theoretical results.