This short activity simulates the outbreak of a disease, the symptom of which is standing up.

The objective is to see how quickly the disease spreads across the classroom. This will help students to understand that it doesn’t take many steps for an outbreak to spread through an unvaccinated population.

**Resources:** Slides (

PowerPoint or

PDF)

**Curriculum Links**
Maths:

- Recognising geometric sequences and finding the $n^{\text{th}}$ term.
- Recognising powers of 2, 3, 4 and 5.

### Aims

- To teach students about the concept of infectious disease transmission.
- To introduce students to the concept of exponential growth.
- To understand the potential impact of such a disease.
- To introduce the concept of a reproduction number for a disease – $R_0$
- The value of $R_0$ at any given time will indicate if the outbreak is growing or in decline.

### Activity (Whole Class)

Start with the whole class sitting down. Ask for one volunteer to be the first case.

This first volunteer should then stand up and "infect" two classmates by pointing to them.

These two students then stand up, having been infected.

These two students then each infect two others in the classroom, and so on, until the whole class has stood up.

Ask the students how many steps it has taken to infect their class.

### Questions for thought

**Estimate how many steps it would take to infect their school, town, country or the world etc.**
*It takes approximately $33$ steps to infect globe (as there are $2^n$ new cases in generation $n$ of the outbreak).*
**If they repeat the outbreak, with a different person starting, will they get the same result?**
**What would happen if each person pointed to 3 or 4 people instead of 2?**
**What can this tell us about how infectious diseases spread?**
**What are the limitations of this simulation of an outbreak?**
*It assumes that everyone is susceptible to infection and that exactly 2 people get infected each time.*
**Discussion of concept of $R_0$ (the standing disease has $R_0 = 2$).**
Explain relationship between $R_0$ and $1$ – whether an outbreak is increasing or declining (see

$R_0$ Game for a development of this).

### Case Study: 77 Million Cases of Smallpox!

*“Eyebrows were raised when the (United States’ Public Health Agency) Center for Disease Control’s model forecast a potential 77 trillion cases of smallpox if it were ever to be accidently released from a laboratory and the epidemic went unchecked.”*
Ben Cooper (2006)

77 trillion cases far out-numbers the population of the globe – therefore the modeller of this potential outbreak appears to have got carried away with his simulation. This reminds us that we need to question our models when calculating how big an outbreak might become.

Such an example should act as a reminder to students to check their answers to ensure they are reasonable answers to give.