An analysis of a SIRS model with isolation on complex network

The research on immune strategy of epidemic spreading mostly based on simulation data which were lack of theoretical support. The paper was born to establish an improved SIRS epidemic model with isolation factor on both uniform network and scale-free network. We had got the disease-free equilibrium and proved the existence of the endemic equilibrium as well as its uniqueness. We also analyzed the stabilization of the system near the disease-free equilibrium and endemic equilibrium by Lyapunov stability theory. Finally we discussed the influence on the spreading of epidemic carried by isolation factor and structure of network which were supported by the simulation.