A colored mean-field model for analyzing the effects of awareness on epidemic spreading in multiplex networks - Wu, Qingchu (2019)
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. Network epidemiology involves individual contact information and behavioral response. It should be meaningful to study how the epidemic information-based behavioral response affects the epidemic spreading. We can assume that an individual promptly obtains relatively accurate information from the current circumstances and responses to the epidemics via reducing its susceptibility. Generally, the information network may not be exactly the same as the contact network and yet there may exist remarkable link overlap between the information and contact networks. Hence, a multiplex network framework can be used to analyze the influence of awareness on the epidemic spreading. To solve the theoretical analysis problem, we develop an edged-colored heterogeneous mean-field approach and derive the threshold value of epidemic outbreak. By doing so, we can analyze the effects of the link overlap and inter-layer degree correlation between the information and contact layers. It is found that only epidemic information, being available in network nodes’ neighborhood overlapping in two layers, helps change the epidemic threshold.