Global stability of a delayed HIV-1 dynamics model with saturation response with cure rate, absorption effect and two time delays

Abstract

In this paper, we proposed a new HIV-1 infection model with saturation infection rate by incorporating, cure rate, absorption effect, and two-time delays namely intracellular time delay that representing the time viral passage into a target cell and creation of new infectious particles and maturation time delay representing the required time for newly produce virus to mature and the infect the susceptible cell. The mathematical investigation shows that the basic reproduction number R0 of the model totally decides the steadiness properties. Utilizing the characteristic equation of the model and Routh-Hurwitz steadiness basis, we affirmed that the infection-free equilibrium and the chronic disease equilibrium are locally asymptotically steady in case R₀ ≤ 1 and R₀ > 1, individually. If R₀ ≤ 1, using the appropriate Lyapunov functions and LaSalle’s invariance principle, it has been shown that the infection-free equilibrium of the model is globally asymptotically stable. If R₀ > 1 the model is persistent. Conversely, if R₀ > 1, the infection-free equilibrium is unstable and a unique chronic infection equilibrium exists. We show that, if R₀ > 1, the chronic infection is globally asymptotically stable. Moreover, numerical simulations are performed to verify the theoretical results.