Modeling and Analysis for a Delayed Cytokine-Enhanced Viral Infection Model

In this paper, we propose a delayed viral infection model to incorporate a logistic proliferation, a cell pyroptosis effect and the three intracellular time delays. We present the basic reproduction number and investigate the existence and the global stability of equilibria: infection-free equilibrium [Formula: see text] and infection equilibrium [Formula: see text], respectively. By considering different combinations of the time delays, we investigate the existence and the properties of Hopf bifurcation from [Formula: see text] when it is unstable. We also numerically explore the viral dynamics beyond stability. Bifurcation diagrams are used to show the stability switches, multiperiod solutions and irregular sustained oscillations with the variation of time delays. The results reveal that both the logistic proliferation term and time delays are responsible for the rich dynamics, but the logistic proliferation term may be the main factor for the occurrence of the Hopf bifurcation. Moreover, we show that ignoring the cell pyroptosis effect may underevaluate the viral infection risk and the sensitivity analysis implies that taking effective strategies for reducing the impact of cell pyroptosis is beneficial for decreasing the viral infection risk.