Rendezvous effects in the diffusion process on bipartite metapopulation networks.

Epidemic outbreaks have been shown to be closely related to the rendezvous-induced transmission of infection, which is caused by casual contact with infected individuals in public gatherings. To investigate rendezvous effects in the spread of infectious diseases, we propose an epidemic model on metapopulation networks bipartite-divided into two sets of location and rendezvous nodes. At a given transition rate γ(kk')(p), each individual transfers from location k to rendezvous p (where rendezvous-induced disease incidence occurs) and thereafter moves to location k'. We find that the eigenstructure of a transition-rate-dependent matrix determines the epidemic threshold condition. Both analytical and numerical results show that rendezvous-induced transmission accelerates the progress of infectious diseases, implying the significance of outbreak control measures including prevention of public gatherings or decentralization of a large-scale rendezvous into downsized ones.