Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response

Abstract

In this paper, a cytokine-enhanced viral infection model with time delays and CTL immune response is proposed and analyzed. Multiple time delays, namely intracellular delay τ1, virus replication delay τ2 and immune response delay τ3 are included. Firstly, two key parameters with strong biological significance, namely the virus reproductive number R0 and the CTL immune reproductive number R1 are derived. And then the stability of equilibria of the model is investigated by constructing suitable Lyapunov functionals and using LaSalle’s invariance principle. We prove that if R0<1, then the infection-free equilibrium E0 is globally asymptotically stable for any τ1,τ2,τ3≥0; if R0>1,R1<1, then the immunity-inactivated equilibrium E1 is globally asymptotically stable for any τ1,τ2,τ3≥0; and if R1>1, then the immunity-activated equilibrium E∗ is globally asymptotically stable for any τ1,τ2≥0 and τ3=0. For τ1,τ2≥0,τ3>0, theoretical analysis and numerical simulations show that with the increase of τ3, the equilibrium E∗ loses its stability and the system generates Hopf bifurcation, which means the system produces periodic oscillation under certain conditions.