Epidemics on networks

This activity simulates how an infectious disease may spread through a social network.

For epidemiologists it is important to know not only the number of cases that any one case may infect ($R_0$), but also how the outbreak may spread through a population. As such, it is vital to understand the dynamics of a community or population.

This is done by looking at how individuals interact with each other - i.e. who comes into contact with whom, and how often. Mathematical modellers can then build this into their simulations to understand how an outbreak has spread through a population.

This is vital for health researchers to understand, as it helps them to to contact trace individuals who may have become infected, so as to stop an outbreak spreading further.

Resources: Slides (PowerPoint or PDF), dice, Printable network template (PowerPoint or PDF)

Curriculum Links

Maths:

• Calculating the probability of independent and dependent combined events
• Modelling situations mathematically

Aims

• To understand social network structure
• To understand how an infectious disease will spread differently depending on where it is started in the network.

Activity (Whole Class)

Introduce networks

Show the first slide with the two different networks. Ask students what they think the difference is (Answer: Age).

Discuss why these networking patterns may be different over time.

Show romantic network in US high school to spur further interest (optional)

Activity (Pair work)

Separate the class into pairs or small groups. Distribute print outs of the network, along with a dice to each pair/group.

Everyone starts off susceptible; pick one point of the network on the print out to be the first infected person.

Go around the infected person's contacts in turn. For each one, roll the die, if they get a 1 or a 2, that person also becomes infected. If it is anything else, they are immune.

Repeat for the new infected cases - and so on, until the epidemic ends.

Count how many cases are infected, and how many steps it took to infect the group.

Repeat the exercise several times, with different starting points. Note down the number of cases in each time

This data can then be used for further analysis - mean, median, mode, distribution, epidemic curve etc. Get students to plot graphs and analyse their results amongst their small group - or as a whole class. 

Questions for thought

How/Why does the social network change between 4-5 year olds and 10 -11 year olds?

Would you expect this network to change again for 16 year olds? What about for adults?

What do the individual nodes in the network represent?

It might not be that they don't have any friends! They may have been absent on the day the data was collected, their contacts may not have consented to the study etc.

Does the romantic network in the US high-school surprise you?

Why are we only infecting those nodes when a 1 or 2 is rolled?

This is to take into account that not everyone in a network will necessarily be susceptible to a disease

What would happen if we allowed 1, 2, 3 or 4 to infect someone?

What happens if you start in different places around the network?

Why does the outbreak change in size each time it is simulated?

Extension Activity: Targeted Vaccination (Whole Class)

Who would you vaccinate in the network?

If you only had 2 or 3 doses of vaccine for the network, who would you choose to vaccinate and why?

Would you protect people with the greatest number of links / break the network in certain places?

Students can do this individually and then feedback to the whole class.