Hybrid Control on Stability and Bifurcation for a Delayed Complex Networks Fractional-Order Model of Disease Spreading

This paper explores the Hopf bifurcation behavior of a general nonlinear disease spreading model with hybrid control. When hybrid control is applied to the system, the stability of the system can be significantly improved by adjusting the controller parameter. Firstly, the characteristic equation is circumspectly researched by choosing time delay as the bifurcation parameter, and the criteria is derived for the stability and Hopf bifurcation of the system under hybrid control. Then the bifurcation diagram and stable area of the system is obtained through numerical simulation. We also found that link-adding probability, fractional order and nonlinear interaction coefficient can also effectively influence the dynamic behavior of such networks. And with the decrease of these system parameters, the stability of the system is improved. Finally, the validity of the conclusion was verified through sensitivity analysis.