Periodic Epidemic Spreading over Complex Systems: Modeling and Analysis

It is well observed that some infectious diseases show a feature of periodicity; that is, the disease may prevail during a certain season and vanish afterwards. In the effort of understanding this specific phenomenon, in this paper, we propose a spreading model with a time-variant infectivity function considering both the features of periodicity and agent variability. We apply the modified model to a scale-free network frame with tunable power-law coefficient to find out the characteristics of periodic spreading dynamics. Our work consists of both theoretical derivation and a series of corresponding numerical simulations in order to find out the influence of the parameters of both network topology and the modified model on spreading dynamics in the underlined networks. The experiments prove the success of our model in producing a periodic behavior of spreading, and the results agree well with theoretical calculations.