| Complex networks is a subject that full of life and wide application. Recent years have witnessed great advancement in this active field of statistical physics.We summarize the definition, the development history and the application foreground of the complex networks, and introduce the basic topology parameter which can be described the characteristic of the network and the classical network model, moreover expound several classical epidemic models and the dynamics on small-world and scale-free networks.We pay more attention to the interplay between the topology and the epidemic dynamics on scale-free networks. In order to obtain the interaction about them, we choose the typical BA model as the network model and a susceptible-infected-susceptible (SIS) model as the spreading process, and we study the interplay between the topology and SIS model on BA networks by the way of computer numerical simulation. We acquire the following conclusions by the simulations:(a),Aspect of the topology of the network:Due to self-protect rewiring, the degree distribution shows exponent cut-off power law and exponential degree distribution, while the clustering coefficient displays fluctuated behavior and the uncorrelated characteristic isn't changed.(b),Aspect of the rule of epidemic evolution :1)There exist a threshold pc of spreading probability. Above the threshold, the infection can diffuse and persist in the network and arrive at equilibrium eventually. Below it, the number of infected people will reach a peak first, and then decay as an exponent, and recover at last. The threshold decreases with the average degree of the network increasing. 2)The maximum density of the infected grows nonlinearly with p increasing and decreases slowly with the w increasing. 3)The evolution behavior of the SIS model on the static BA networks is more quickly than that on the dynamical networks, indicating that the dynamical network tends to suppress the diffuse of the epidemic.
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