Impact of community structure on the spread of epidemics on time-varying multiplex networks

Community structure plays a crucial role in realistic networks and different communities can be created by groups of interest and activity events, and exploring the impact of community properties on collective dynamics is an active topic in the field of network science. Here, we propose a new coupled model with different time scales for online social networks and offline epidemic spreading networks, in which community structure is added into online social networks to investigate its role in the interacting dynamics between information diffusion and epidemic spreading. We obtain the analytical equations of epidemic threshold by MMC (Microscopic Markov Chain) method and conduct a large quantities of numerical simulations using Monte Carlo simulations in order to verify the accuracy of the MMC method, and more valuable insights are also obtained. The results indicate that an increase in the probability of the mobility of an individual can delay the spread of epidemic-related information in the network, as well as delaying the time of the peak of the infection density in the network. However, an increase in the contact ability of mobile individuals produces a facilitating effect on the spread of epidemics. Finally, it is also found that the stronger the acceptance of an individual to information coming from a different community, the lower the infection density in the network, which suggests that it has an inhibitory effect on the disease spreading.