Complex Networks On The Spread Of The Disease Behavior

As a powerful tool for the study of complex systems, complex networks have received extensive attention from all communities of science. As known to us all, one of the ultimate goals for studying complex networks is to understand the behaviors on dynamical processes occurring on them. Among various dynamics, disease spreading is one of the most important processes. In this paper, we study in detail the SI (Susceptible-Infective) model for disease propagation on complex networks. The main work and contribution are as follows:First, using the classical SI epidemiological model as propagation rules, we compare the speeds of disease spread in some classic complex networks, including regular networks, Erdos-Renyi (ER) random graphs, Watts-Strogatz (WS) small-world networks, and Barabasi-Alber (BA) scale-free networks. As a result, we find that the topological structures of the networks play important roles in propagation speed. We also analyze the principal reasons for affecting the diffusion velocity. Through simulations, we also find that if the hub nodes in scale-free networks or vertexes in small-world networks are firstly infected, the spread rates will be quickened in respective networks.The second work of the present paper is investigating the influence of power-law degree distribution itself on the diffusion behavior of disease on scale-free networks. To this end, we introduce a family of scale-free network model controlled by a parameter q. The whole family of networks exhibits the same degree distribution, zero clustering. In particular, when q increases from 0 to 1, there are a crossover between small-world and large-world and a transition from non-fractal to fractal. Our study shows that, when q grows from 0 to 1, there exits a transition from hierarchical infection to non-hierarchical infection. Thus, the power-law degree distribution does not suffice to characterize the dynamical behaviors of disease diffusion on scale-free networks.