LAUSR

Abstract The contacting heterogeneity is crucial for the propagation of directed transmitted infectious diseases. Here we construct a stochastic model on the level of subgroups which are classified according to the activity degrees of the hosts. Using the central limit theorem, we present the analytical results concerning with the fluctuations around the outbreak prevalence. In particular, we get the forms of the covariance matrix for Gaussian random diffusions as well as the laws of outbreak prevalence for SIR epidemics. So that the analytical distributions for the outbreak prevalence of the SIR epidemics in complex networks are presented, which can be used in outbreak prevalence predicting and transmission intensity inferring.