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This problem belongs to the Contagious Maths: Understanding the Spread of Infectious Diseases collection. It follows on from Build your first model and Lucky Dip.
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):
And different shapes represent people who are infected, recovered or immunised:
To run your first simulation, click the "Infect a random person" button
You'll see that one person has turned red, it means they have been infected and are liable to spread the disease to people near them.
What do you think will happen next? Can you justify your answer?
You can now investigate whether you were correct, by either watching the epidemic progress one generation at a time, by clicking on the 'Run a generation' tab, or letting it run its course and seeing the outcome, by clicking on 'Run to the end'. Note that when someone turns purple, it means they have recovered from the disease and are immune to it.
Explore the interactivity by infecting random or selected individuals, immunising selected individuals, and varying the value of R.
Notice if you change R, the mix of different colours changes to make up the right value for the mean.
Can you anticipate what will happen?
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?
In this video clip, Julia explains why R is important to understanding epidemics, particularly whether R is greater than or less than 1.
What else do you think should be taken into account in order to improve the model?
This concludes Part 3. These resources continue with Part 4: Get Moving!, which will introduce models where the population moves about. Alternatively, if you are finishing here, you make like to continue to Wrap up and Meet the Researchers.
In the Teachers' Resources section you will find suggestions as to how this material might be used in the classroom.
This is the third 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.