Part 4: Get moving!
Here we make the model more realistic, by exploring the effect of movement by a population on the spread of an infectious disease. There's an interactivity that allows you to party, commute, and visit friends.
Problem
This problem belongs to the Contagious Maths: Understanding the Spread of Infectious Diseases collection. It follows on from Build Your First Model, Lucky Dip and Everybody is Different.
Connections
You can change the layout by clicking the purple cog, selecting a layout, and then clicking one of the two buttons at the bottom of the settings.
- How does a disease spread differently when people are evenly spaced out in a square grid rather than a hexagonal pattern (select “Grid” layout)?
- What about when they are arranged in satellite cities that are linked together (select “Satellites” layout)?
- Or when they are in several suburbs connected to a main city (select “Suburbs” layout)?
Moving on...
In this video clip, Julia points out that disease modellers need to consider how diseases spread across different communities when people move around.
The interactivity below enables us to simulate the outbreak of an infectious disease when populations are mobile.
The key is the same as before: circles represent different people who are susceptible to infection. The colours represent different numbers of nearby people that they could go on to infect (also given by the number displayed on the icons):
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0 contacts (very cautious!)
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1 contact
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2 contacts
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5 contacts (super-spreaders!)
And different shapes represent people who are infected, recovered or immunised:
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are infected and might infect others - and there is a timer bar underneath to show how long through their infection they are
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have recovered from infection and are now immune
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are people that you have chosen to immunise (see below), so are also immune
Can you anticipate what will happen?
You can change the setting by clicking the purple cog, selecting a layout, and then clicking one of the two buttons at the bottom of the settings.
- Party - separate households all converge in a large central space and mix heavily.
- Visitors - some members of some households move about in a large common area.
- Commute - household members travel to a central space and return back afterwards.
- Mixed - most household members travel to a central space and return back afterwards.
When the model has finished, use the Graph button to view a graph of the whole infection from start to finish.
Is it similar to the shape of the graphs in Lucky Dip?
This concludes Part 4. Please continue to Wrap up and Meet the Researchers.
How schools can use these resources
In the "Teachers' Resources" section you will find suggestions as to how this material might be used in the classroom.
This is the last of four parts, designed to be used in a sequence of lessons - here is a lesson by lesson breakdown.
These Contagious Maths resources were developed and written by Julia Gog and the MMP team, including both NRICH and Plus, and funded by the Royal Society’s Rosalind Franklin Award 2020. We have tailored these resources for ages 11-14 on NRICH, and for older students and wider audiences on Plus.
Teachers' Resources
This is the last of four parts, designed to be used in a sequence of lessons - here is a lesson by lesson breakdown.
Why do this problem?
Get Moving! follows on from Build Your First Model, Lucky Dip, and Everybody is Different, and introduces the need for more realistic models, which take into account how people are connected to each other, both in static environments, and when they move around. Students are encouraged to use the interactivity to explore the similarities and differences that occur when running several simulations of the updated disease models.
This lesson, and the previous one, meet the curriculum aims of developing students' Fluency (moving freely between different representations), Reasoning (making connections between number relationships and graphical representations), and Problem Solving skills (begin to model situations mathematically).
The teaching materials include video clips in which Professor Julia Gog points out that models need to take into account how diseases spread across different communities when people are spaced differently, and when people move in different settings.
Possible approach
Get Moving! is intended as a follow-up activity for students who have explored Build your first model, Lucky Dip and Everybody is different.
Start by watching this video clip in which Julia Gog highlights the need for models to take into account where we are spending our time - in homes, classrooms, workplaces, neighbourhoods... Different spatial arrangements can be represented in the models we use, to gain a more realistic understanding of how diseases spread in different contexts.
Revisiting the interactivity from Everybody is Different will offer students the opportunity to explore how the spread of a disease differs when people are spaced differently.
The R slider can be used to change the value of R, and the layout can be changed by clicking the purple cog, selecting a layout, and then clicking one of the two buttons at the bottom of the settings.
- Hexagonal - most nodes have 6 neighbours, closely packed. This gives a lot of scope for infections.
- Grid - most nodes have 4 neighbours, there is less scope for infections to spread.
- Theatre - this is a somewhat realistic layout, to help imagine how disease might spread in a large venue.
- Satellites - an abstract layout, where radial lines of nodes connect large clusters.
- Suburbs - a somewhat realistic layout, to help imagine how infection might spread through cities and villages.
How does the layout affect the spread of the disease?
Next, watch this video clip, which points out that models need to take into account the impact that travel can have in spreading an infectious disease across different communities.
Introduce the Get Moving! interactivity
Do diseases spread differently when people are moving?
Key questions
Do diseases spread differently when people are moving?
What else could we consider exploring with our model?
Possible support
Students could take screenshots to help them compare the outcomes of the spread of the disease each time they run the model.
Possible extension
Please continue to Wrap up and Meet the Researchers for a short concluding video and also clips from individual researchers to explore.
Students may be interested in Disease modelling for beginners, a collection of articles which explain how mathematics helps us understand how infectious diseases spread.
Students could research the story of the village of Eyam, which cut itself off from other communities to protect itself from the 1665-1666 plague.
Students might also be interested in this article by Professor Chris Budd OBE, which explores the differences between models and simulations.
These Contagious Maths resources were developed and written by Julia Gog and the MMP team, including both NRICH and Plus, and funded by the Royal Society’s Rosalind Franklin Award 2020. We have tailored these resources for ages 11-14 on NRICH, and for older students and wider audiences on Plus.