Using networks to predict who gets the flu
An interesting concept in networks is the Friendship Paradox, which states in simple words that your friends have more friends than you do. This can be seen from a simple representation of a small group within a social network like Facebook. Let us consider five friends, A, B, C, D and E such that a graphical representation of their friendships looks like the diagram (link below):
From the diagram, we obtain the following information:
| Person | Number of friends | Number of friends of friends | Average friends of friends |
| A | 1 | 4 | 4 |
| B | 4 | 1+2+2+1 = 6 | 1.5 |
| C | 2 | 4+2 = 6 | 3 |
| D | 2 | 4+2 = 6 | 3 |
| E | 1 | 4 | 4 |
| Total | 9 | 26 | |
| Mean | 1.8 | 2.89 |
We can see that the average number of friends of friends is 2.89 whereas the average number of friends per person is 1.8, which implies that the average person in the group has 1.8 friends but the average friend in the group has 2.89 friends, and this generalizes the friendship paradox which states that the average friend of a person has more friends than the average person.
Now, coming to the interesting part, the friendship paradox has useful applications and one such application is to predict who contracts the flu during a flu outbreak. This originated as an experiment by two social scientists, Nicholas Christakis of Harvard University and James Fowler of the University of San Diego, California who used the friendship paradox to predict the spread of the H1N1 virus in 2009.
From the table above, we see that the “average friends of friends” column is higher than the number of friends for the average friend (2.89) for every person except B, for whom the value is 1.5. This arises due to the fact that B has a lot of friends and it is obvious that a popular person like B would have more friends than his or her friends would. To use this very property of popular persons is the basis of Christakis and Fowler’s social experiment. The two social scientists attempted to prove that people with a lot of connections in a social network catch the flu before those with fewer connections do and hence concluded that the spread of the flu in a social network can be monitored by tracking the health of its well-connected members.
Christakis and Fowler randomly selected a sample of 319 students and asked each of these students to name their friends. It is intuitive to assume that the people that students would name as friends would tend to be popular people, as students would not generally name people who do not have a good number of friends. In total, the researchers got a sample of 425 friends from the student sample. Hence, they got a total sample size of 744 and by monitoring the health of each member of this sample, they were able to discover that persons from the friends sample showed signs of the flu 14 to 69 days prior to the detection of symptoms in the sample of 319 selected students.
This experiment clearly shows that it is possible to determine the spread of a flu outbreak by using the analysis of social networks to determine who the most well-connected members of a social network are, and track their health. Consequently, the study of networks would helping minimizing flu outbreaks by allowing researchers to identify who exactly would be the best candidates for vaccination before a flu outbreak to prevent its spread.
We can also apply the concept of strong and weak ties to this phenomenon to get an estimate of levels of interaction between people in a social network to determine how likely well-connected people in a social network would be to contract the flu to different members of the network and hence, allow us to get an idea of who would be next best candidates for vaccination to minimize the flu outbreak. But while analyzing the strength of ties between friends might be a complicated and tedious procedure, we can conclude that the study of social networks at least easily enables us to figure out the source of the spread of the flu and help minimize its outbreak.
Sources:
http://news.sciencemag.org/sciencenow/2010/09/social-network-predicts-flu-spre.html
-AS24
Using network concepts to help explain the spread of the flu was very interesting. It is common to hear how certain viruses spread throughout the world, but is was great to see how string and weak ties of a social network plays a role in how the virus spreads.