SEIR Epidemic Dynamics in Random Networks

Predicting disease transmission on complex networks has attracted considerable recent attention in the epidemiology community. In this paper, we develop a low-dimensional system of nonlinear ordinary differential equations to model the susceptible-exposed-infectious-recovered (SEIR) epidemics on random network with arbitrary degree distributions. Both the final size of epidemics and the time-dependent behaviors are derived within our simple framework. The underlying network is represented by the configuration model, which appropriately accounts for the heterogeneity and finiteness of the degree observed in a variety of real contact networks. Moreover, a generalized model where the infectious state of individual can be skipped is treated in brief.