Effect of Heterogeneity of Vertex Activation on Epidemic Spreading in Temporal Networks

Development of sensor technologies and the prevalence of electronic communication services provide us with a huge amount of data on human communication behavior, including face-to-face conversations, e-mail exchanges, phone calls, message exchanges, and other types of interactions in various online forums. These indirect or direct interactions form potential bridges of the virus spread. For a long time, the study of virus spread is based on the aggregate static network. However, the interaction patterns containing diverse temporal properties may affect dynamic processes as much as the network topology does. Some empirical studies show that the activation time and duration of vertices and links are highly heterogeneous, which means intense activity may be followed by longer intervals of inactivity. We take heterogeneous distribution of the node interactivation time as the research background to build an asynchronous communication model. The two sides of the communication do not have to be active at the same time. One derives the threshold of virus spreading on the communication mode and analyzes the reason the heterogeneous distribution of the vertex interactivation time suppresses the spread of virus. At last, the analysis and results from the model are verified on the BA network.