Abstract:Objective This paper studied the dynamical characteristics of a virus immune infection models under the influence of immune intensity and time delay. Methods First, we determined the critical value of immune intensity through theoretical derivation and used numerical simulations to verify that the virus immune system underwent saddle node bifurcation at this critical point. Second, we constructed a virus immune model with time delay, solved the equilibrium points using linear stability analysis, and determined the stability of these equilibrium points based on the sign of the real part of the characteristic roots. Finally, we studied the impact of time delay on dynamics. Results The equilibrium points of the system with delay include saddle, stable node, stable focus, and unstable node. It implied that system exhibited bistable phenomena. The stable focus became unstable as the delay increased, leading to Hopf bifurcations. The system transitioned from a stable convergent equilibrium to a periodic oscillatory state, ultimately resulting in a viral outbreak. The stability of unstable node is unaffected by time delay, but the system"s final convergence may have changed with increasing time delay. Conclusions The results of the study are helpful to further understand dynamic mechanisms of virus immune infection system, and provide a theoretical basis for formulating reasonable and effective treatment strategies.