I hope to supply a more complete answer later, but in the meantime I did write a blog post on (or at least related to) this issue:

http://legiononomamoi.wordpress.com/2014/08/06/outbreak-were-all-going-to-die-of-ebola-or-the-movie-outbreak/

Thanks Andrew, i will read your blog post. Elsewhere, another scientist wrote that chimp's antibody is the answer for ebola, like in the outbreak movie. But i read in WHO's webpage that there is no cure yet for ebola. Your further reply is welcome. Thanks

The answer and post of Andrew is interesting and describes the structure of the network for the ebola spread: people can be infected sharing body fluids. This may happen via sexual partners, sharing drinking glasses, kisses, etc., that is, the spread is via intimates. The question now is if intimacy network is scale-free. I am working on that and I cannot give you an answer, but my conjecture is that the answer is no. 

Thank you, Rafael. Best wishes

Besides the intimacy network, other factors should be considered. The network structure provides only the paths where some dynamic process takes place. Some sort of "interaction" between two nodes of the network has to be incorporated in the model in order to simulate the dynamics.

Thank you, Adauto. So do you think that scale free network cannot represent what happens with ebola epodemic?

Best wishes

I am inclined to agree with Villanueva's answer. A scale free network has a rather broad  distribution of links, hubs and so on. My previous answer add another needed ingredient  to properly describe the epidemic process.

Ok thanks. Best wishes

There is evidence that intimate contact is scale-free (admittedly in this paper the graph is also bipartite). If it is true of sex, then why no of less intimate contacts - as mentioned above. There is a heap of literature on the mathematical analysis of such systems (including my own recent book and an excellent review by Pastor-Satorras/Vespignani on arXiv.

Article The Web of Human Sexual Contacts

Thanks, Michael. Best wishes

The concept of scale-free networks has to be used with caution.  I would not dare conclude nor classify an epidemic like ebola as following the scale-free property. This is simply because we know too little (or at least i know too little) about the modes of spread of the disease or any other associated dynamics in its spread,  let alone the biomedical complexity of the mutations that the virus exhibits. Broadly speaking,  i suppose ebola has a pseudo- scale-free degree distribution property in its network,  more work is required to consolidate this conclusion. I hope this helps,  and am curious of what the rest think.

@Jimmy: thanks for your answer. Best wishes

You are not telling us scale-freeness of what network. If you refer to the social network, clearly this can have an enormous impact on epidemic spreading. At the beginning of the works about epidemic spreading modeling and simulation, the social network was not considered, and using SIS and SIR models researchers arrived to the conclusion that there is a threshold infectivity meaning that if a pathogen has an infectivity lower that the threshold, the epidemic will fade out in time; however, when starting the use of mean field models and later by taking into account realistic structures of the social network, researchers have realized that this threshold is non-existent. Therefore, simply adding the topology of the social network over which the epidemic spreads has revealed that pathogens with minimal infection rate can globally spread. The structure of the social network can be moreover be used proficiently for targeted vaccine campaigns, whereby social hubs are targeted first.