# Maths and the Spread of Infectious Diseases Session 4: the Ticket Conundrum

#### Possible approach

Video clip 1 - reflect on previous learning re AP/GPs, maths v reality eg infinity, importance of chosing the right factors for models so they are helpful. So far, models have been static - at home, in a classroom etc - with  a specific group of people - but we tend to mix with different groups during the day. need dynamic approach which more accurately reflect the way we live our lives by mixing with others.

#### Main activity

*It would be helpful for NRICH to film short video modelling use of the interactivity Dynamic Disease Model interactivty for this session*

Begin by asking the class to list the different groups they mix with each day  - these typically include commuters on public transport, their year group, their class, their lunchtime club, their after school club, their family, their friends after school and may be after school clubs.

In today's lesson, the class will explore the spread of an infection when people mix in different settings such as homes in the same street or when they are commuting to school or work, just as the learners do each day. Understanding what happens to the spread of a virus when we mix helps officials make the best informed decisions to keep us safe.

Prepare to share the NRICH video clip showing how the 'Visitors' interactivity works - the team model it when the street has no infectious outbreaks but the visitors are infectious - what might happen? Watch the video to see if you're right.

Allow time for the class to explore the interactivity on the default 'Visitors' for themselves, first running the same scenario as above to build their confidence using the interactivity and compare their results across the class when different groups run the same model. Then discuss what they might suggest the options local authorities might have to consider to prevent such outbreaks.

Then explore the opposite scenario where the households are infectious but not their visitors. This links to the real-life scenario during the Black Death in 1665-1666 when the infection arrived in the small Derbyshire village of Eyam. It was a similar situation to this model - villagers living together in homes, visitors from outside the local area coming to deliver essentials to their communities. How might they have managed the situation? You can read more about the difficult decisions that the villagers made, and their consequences, here.

Video clip 2 - could Julia discuss how modellers faced questions about households meeting in the family home, such as at Christmas, mark the end of Ramadan and other family occassions? Perhaps also mention sports tournaments such as football matches when we might gather in homes with friends to watch a game, then move to another friend's house to watch the next game,

Still working with 'Visitors' setting, encourge class to consider one possible option - vaccination. Allow time for them to test the effect of vaccinating different groups - stay at homes v movers. Do they need to vaccinate them all? Who should get vaccinated first and why? They may also wish to explore the effect of varying the r number.

The interactivity has four settings. Now move on to consider a different scenario where all the people mix - a local event ('Village' setting). Model changing the setting and allow class time to explore the new scenario. Then encourage class to discuss ways that they might suggest people behave to reduce the spread of infection eg vacinnation. Allow time to investigate who they might suggest should be vaccinated to reduce an outbreak and justify their answer. They may also wish to explore the effect of varying the r number.

Video 3 clip - could Julia discuss her expereinces of modelling local events at this point where everyone mixes together? Perhaps also discuss impact findings ight have the decisions that are taken by schools and government relating to large events where many people might mix from different households.

Discussion about differences between the 'Visitors' and 'village' settings - what's the same/what's different - draw out that everyone moved around in the 'village model but not the 'visitors' model. The visitors model might work for special events eg Chistmas, but our daily lives often revolve around commuting so our third scenario for classes to explore is the commute to school and work, often known as 'the school run.' Unlike 'visitors' model, the 'commuters' come back. Not everyone in a street, of course, does the school run - some people are working from home or elderly and do not need to leave. Explore what happens if there's one infected person, then allow time for the class to explore the same scenario and compare results.  Again, the class can discuss possible ways to restrict the spread of the disease and explore the impact of vaccinating different people to decide on a possible course of action and justify it. They may also wish to explore varying the r number. Learners may also wish to explore the 'Commute' setting where everyone travels on the same day - this is quite similar to the situation they may encounter, or older siblings may be encountering, when they are a little older and living away from home in student digs and travelling into college or university each day.

Video clip 4  - this clip pulls everyhting together from the 4 sessions including important messages about the reason we need mathematical modellers and how their maths skills can help very large numbers of people protected, it's a key way maths can help people and keep them safe. Also note that modelling is not about getting the 'right' answer, but using mathematics to help us to make better decisions. It can help us identfiy useful straetgies, but life is messy!

### Possible follow-ups

Lesson 5 encourages classes to go further and behave like many researchers by designing a poster sharing their finding from this project (many researchers share their work through posters at conferences - these posters are very visual, explaining their work and ideas - and conference visitors can tour the conference hall to read them and ask questions to the researchers who are usually standing by their posters).