Edge-based SEIR dynamics with or without infectious force in latent period on random networks

In nature, most of the diseases have latent periods, and most of the networks look as if they were spun randomly at the first glance. Hence, we consider SEIR dynamics with or without infectious force in latent period on random networks with arbitrary degree distributions. Both of these models are governed by intrinsically three dimensional nonlinear systems of ordinary differential equations, which are the same as classical SEIR models. The basic reproduction numbers and the final size formulae are explicitly derived. Predictions of the models agree well with the large-scale stochastic SEIR simulations on contact networks. In particular, for SEIR model without infectious force in latent period, although the length of latent period has no effect on the basic reproduction number and the final epidemic size, it affects the arrival time of the peak and the peak size; while for SEIR model with infectious force in latent period it also affects the basic reproduction number and the final epidemic size. These accurate model predictions, may provide guidance for the control of network infectious diseases with latent periods.