Dynamic stability and optimal control of SIS [Formula: see text] I [Formula: see text] RS epidemic network()

We develop a complex network-based SIS [Formula: see text] I [Formula: see text] RS model, calculate the threshold [Formula: see text] of infectious disease transmission and analyze the stability of the model. In the model, three control measures including isolation and vaccination are considered, where the isolation is structured in isolation of susceptible nodes and the isolation of infected nodes. We regard these three kinds of controls as time-varying variables, and obtain the existence and the solution of the optimal control by using the optimal control theory. With regard to the stability of the model, sensitivity analysis of the parameters and optimal control, we carry out numerical simulations. From the simulation results, it is obvious that when the three kinds of controls exist simultaneously, the scale and cost of the disease are minimal. Finally, we fit the real data of COVID-19 to the numerical solution of the model.