Impact of delay on HIV-1 dynamics of fighting a virus with another virus

الأصل · EN

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number R₀ are identified and its threshold properties are discussed. When R₀ < 1, the infection-free equilibrium E₀ is globally asymptotically stable. When R₀ > 1, E₀ becomes unstable and there occurs the single-infection equilibrium Eₛ, and E₀ and Eₛ exchange their stability at the transcritical point R₀ =1. If 1< R₀ < R₁, where R₁ is a positive constant explicitly depending on the model parameters, Eₛ is globally asymptotically stable, while when R₀ > R₁, Eₛ loses its stability to the double-infection equilibrium Ed. There exist a constant R₂ such that Ed is asymptotically stable if R₁<R₀ < R₂, and Eₛ and Ed exchange their stability at the transcritical point R₀ =R₁. We use one numerical example to determine the largest range of R₀ for the local stability of Ed and existence of Hopf bifurcation. Some simulations are performed to support the theoretical results. These results show that the delay plays an important role in determining the dynamic behaviour of the system. In the normal range of values, the delay may change the dynamic behaviour quantitatively, such as greatly reducing the amplitudes of oscillations, or even qualitatively changes the dynamical behaviour such as revoking oscillating solutions to equilibrium solutions. This suggests that the delay is a very important fact which should not be missed in HIV-1 modelling.