Dynamics of discrete epidemic models on heterogeneous networks

In this paper, one considers the discrete epidemic models on heterogeneous networks, stability and bifurcation of the endemic equilibrium of SIS model is studied, the dynamics analysis of SIRS model and the immunization are discussed. Compared with the epidemic model established by differential equations, the difference systems have the same stability conditions at the disease free equilibrium, and the dynamical behaviours of endemic equilibrium is more complex for discrete epidemic model. These obtained results can be used to explore the complex epidemic propagation dynamics on the networks.