Microscopic edge-based compartmental modeling method for analyzing the susceptible-infected-recovered epidemic...

The edge-based compartmental modeling (EBCM) approach has been used widely to characterize the nonrecurrent epidemic spreading dynamics (e.g., the susceptible-infected-recovered model) in complex networks. By using the probability theory, we derived an individual-based formulation for this approach, which we herein refer to as the microscopic EBCM method. We found that both for small and large initial infection numbers, the epidemic evolution agreed well with the ensemble averages of our stochastic simulations on different complex networks. Moreover, we showed that the dynamical message passing model, the standard EBCM system, and the pair quenched mean-field equations can be deduced by our microscopic EBCM method. In addition, the microscopic EBCM method was used to analyze the effect of epidemic awareness on networks. Importantly, the simple EBCM model for exponential awareness was developed. Our method provides a way for handling nontrivial disease transmission processes with irreversible dynamics.