Effects of Filippov-type threshold control on a emerging infectious disease model with time delay

In this paper, a delayed mathematical model for emerging infectious diseases with a piecewise control function concerning threshold policy for disease management strategy is proposed. Based on the theory of functional differential inclusions and set-valued analysis, we establish the global existence and boundedness of the solution in the sense of Filippov. Then, the existence and stability of equilibria as well as the direction and stability of local Hopf bifurcation at endemic equilibria for two subsystems are investigated. Next, we analyze some key elements of the model, including sliding segment, sliding mode dynamics and pseudoequilibrium. Through numerical simulations, we discover that our system, owing to the complexity of the model, exhibits some complex dynamical behaviors that have never been previously observed. Finally, through the analysis of sliding mode bifurcation, local sliding bifurcation and global sliding bifurcation, we demonstrate the significant impact of control intensity [Formula: see text], threshold level [Formula: see text] and time delay [Formula: see text] on the dynamics of our model. In summary, our delayed Filippov system provides some new insights into the prevention and control of emerging infectious diseases.