Epidemic spreading in a variety of scale free networks.

We have shown that the epidemic spreading in scale-free networks is very sensitive to the statistics of degree distribution characterized by the index gamma, the effective spreading rate lambda, the social strategy used by individuals to choose a partner, and the policy of administrating a cure to an infected node. Depending on the interplay of these four factors, the stationary fractions of infected population F(gamma) as well as the epidemic threshold properties can be essentially different. We have given an example of the evolutionary scale-free network which is disposed to the spreading and the persistence of infections at any spreading rate lambda>0 for any gamma. Probably, it is impossible to obtain a simple immunization program that can be simultaneously effective for all types of scale-free networks. We have also studied the dynamical solutions for the evolution equation governed by the epidemic spreading in scale-free networks and found that for the case of vanishingly small cure rate delta<<1 the initial configuration of infected nodes would feature the solution for very long times.