Novel epidemic models on PSO-based networks.

This paper proposes two spatio-temporal epidemic network models based on popularity and similarity optimization (PSO), called r-SI and r-SIS, respectively, in which new connections take both popularity and similarity into account. In the spatial dimension, the epidemic process is described by the diffusion equation; in the time dimension, the growth of an epidemic is described by the logistic map. Both models are represented by partial differential equations, and can be easily solved. Simulations are performed on both artificial and real networks, demonstrating the effectiveness of the two models.