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 $\lambda >0\mathrm{}$ 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 $\delta \ll 1$ the initial configuration of infected nodes would feature the solution for very long times.