Analysing Networks

Age 11 to 16

This classroom activity is part of the Disease Dynamics collection

This activity allows students to understand different ways of interpreting the data about social networks, and what this tells us about how individuals interact with each other. It also shows how simple mathematical concepts can help with this analysis.

Knowing how individuals in a certain population interact can allow mathematical modellers to add an extra level of complexity to their models of outbreaks, to offer greater insight into why certain people in a population may be a greater risk of infection if an outbreak begins.

It can also suggest which patterns of social behaviour may need to be changed if an outbreak does begin - e.g. social distancing/ quarantine.

Time: 30 minutes
Resources: Slides (PowerPoint or PDF), Printable Table (PowerPoint or PDF)

Maths:
• Describing, interpreting and comparing observed distributions of a single variable, including graphical representations and mean, median, mode, range and inter-quartile range.
• Constructing and interpreting appropriate tables, charts, and diagrams.
• Constructing and interpreting diagrams for grouped discrete data and continuous data and knowing their appropriate use.
• Applying statistics to describe a population.

Aims

• To understand different methods to analyse data.
• To use network to practice concepts of mean, median, mode, frequency, distribution.
• To learn new analytical concepts for analysis of networks: counting triangles and cliques.

Activity (Small Groups)

Put the first slide up on a screen. Explain to students that this data comes from asking an office of people which two people in the office they spend the most time with.

Next show the second slide - and explain how you can measure contacts in a network; out degree / in degree / mutual. Ask students to draw the rest of the table, so that they have the in-degree, out-degree and mutual contacts. You can use the chart provided and they can populate the extra columns.

Next - ask the students to draw the network in different ways

Analysis

Plot the degree distribution as a histogram (in degree & mutual contacts)

Establish the mean, median and mode

Cliques & Triangles

Explain to the students about cliques & networks

Count the cliques in the network

Count the triangles in the network

Questions for thought

What does this data tell us about our network?

What can a large clique tell us about a population?

How does drawing the network differently alter the way we can see the network / connections?

Why does knowing social interactions help us understand how a disease may spread?
It can help to explain why certain people may get diseases, who may be likely to become infected.

In the first slide, what do the different colours represent?
Boys and girls.

How else could we represent the same data? What do different representations tell us?

Contact Tracing in the ebola virus disease in West Africa (2014-5)

Tracing how an epidemic spreads in a network is vital in all responses to infectious disease outbreaks.

In the ebola outbreak in 2014-15, field epidemiologists needed to make sure they had contacted everyone who had come into contact with an infected person or body. They then were able to monitor these individuals for 21 days (the incubation period of ebola) to see if they developed symptoms.

If they did, these patients would then be isolated, tested and provided care, and the cycle starts again - all of the new patients contacts are found and watched for 21 days (and so on!). Even one missed contact can keep the outbreak going!