Analysis of epidemic models with demographics in metapopulation networks

► In this paper an SIS model on complex networks with constant-inputting is discussed. ► Another SIS model with the logistic form on complex networks is discussed. ► The analysis of the dynamics of two models is given. ► We develop the results of D. Juher, J. Ripoll and J. Saldana in PHYSICAL REVIEW E (80) and J. Saldana in PHYSICAL REVIEW E (78).