Susceptible-infected-recovered epidemics in random networks with population awareness

Microscopic edge-based compartmental modeling method for analyzing the susceptible-infected-recovered epidemic spreading on networks

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.

A colored mean-field model for analyzing the effects of awareness on epidemic spreading in multiplex networks

We study the impact of susceptible nodes' awareness on epidemic spreading in social systems, where the systems are modeled as multiplex networks coupled with an information layer and a contact layer. We develop a colored heterogeneous mean-field model taking into account the portion of the overlapping neighbors in the two layers. With theoretical analysis and numerical simulations, we derive the epidemic threshold which determines whether the epidemic can prevail in the population and find that the impacts of awareness on threshold value only depend on epidemic information being available in network nodes' overlapping neighborhood. When there is no link overlap between the two network layers, the awareness cannot help one to raise the epidemic threshold. Such an observation is different from that in a single-layer network, where the existence of awareness almost always helps.