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Contagion on Graphs

The paper, “Epidemic spreading on complex networks with community structures”, addresses modeling the spread of contagion on complex networks. In class we discussed the spread of contagion on trees which is more ideal than realistic. Very few community structures among people have this perfect structure that makes them easily analyzable; we discussed in class the SIR model can be used, but does not allow for as simple of a result as we found with trees. This study summarizes this difference by exploring the way that structure affects the spread of contagion. They  found that on a macro level the structure of the network had a large effect on how the contagion spread. In essence, how many clusters there are and how connected the clusters are played a large role in modeling the contagion. To study this they used three different models. A very randomized model that would predict the spread of contagion on a tree well, a somewhat randomized model that preserved macro scale features of a network, and the least random model which preserved micro features in a network such as structure with in a cluster. They tested these models on different types of populations including social networks, professional networks, and fungal networks. They found that the most random model fit the fungal population very well, as this structure was tree like. The macro feature preserving model and the micro feature preserving model performed equivalently, but far better than the random model on the human networks. This showed that the structure overall of a network does effect how contagion can spread, but the micro scale things do not affect much. They explained this because with in a cluster the graph is significantly more dense, so the disease will spread significantly better in clusters than outside, but outside the cluster the structure can impair or instigate the spread of disease significantly.

In class we discussed modeling the spread of disease in graphs using the SIR model. This article explains why the simple random model that works well for trees does not simply translate to graphs. The same concepts of a disease spreading over an edge with some probability is preserved, but in a graph the different structure changes how the disease can spread. In the dense clusters the disease is very likely to spread, but between the clusters the comparative scarcity of edges makes the spread more variable, and less predictable by a random model. The placement of edges, the number of edges around a node, and the location of a node (ie inside or outside a cluster), impacts if the contagion is likely to spread to a node.

https://www.nature.com/articles/srep29748

Stegehuis, C. et al. Epidemic spreading on complex networks with community structures. Sci. Rep. 6, 29748; doi: 10.1038/srep29748 (2016).

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