I found a very interesting paper by Fredrik Liljeros, et all titled “Sexual networks: implications for the transmission of sexually transmitted infections” It explains how many epidemiological models which use ordinary differential equation (ODE) to model the spread of sexually transmitted diseases ignore many important details to be able to analytically derive results from these models. However, many of these details are important to really understand how the diseased is spread in a population. For example, one of the assumptions that these ODE models make is that sexual encounters among people are random. However, studies show that this is simply far from being true.

One way to account for these important details in to construct a model by thinking of people as nodes and connect people who have sex by edges. In other words, the idea is to work with a network. By constructing a sex network based on real data, we can get a much better idea of what the dynamics of sexual relationships are like. For example, an important question that a network could answer is the following: Studies show that within each community there is small group of people who have a lot more sex than the rest of the people. Do the people in this group mostly have sex with people within the group, or do they mostly have sex with people outside the group? The answer to this questions has been shown to make a big difference as to how fast and how much a disease spreads. Clearly, understanding these dynamics is very important in order to understand how a sexually transmitted disease spreads.

The authors of this paper make another very good point. If we lived in a completely monogamous world then it would be really hard for sexually transmitted disease to spread since they cannot go from one couple to another couple. Therefore, the most important aspect of sex network for this problem is how many nodes are connected to more than one other node. In other words, it would be better to study a network of concurrent sexual contacts. This new network is called a line graph and it is derived from the original network by making each edge between two people a node and by making an edge whenever one person has more than one contact.

This paper was very interesting because it gave a direct application of networks and also discussed how it is useful to construct a more complex type of graph i.e the line graph to study this specific problem. It can be found at http://amaral.chem-eng.northwestern.edu/.