This investigation has several levels of challenge. You don't have to do it all. Like a video game, you can stop at any level then return later for the next level. Keep good journal notes so you know the level you reached.
The Reproduction Number (R) is the number of people to whom the virus is transmitted by 1 infected person.
When a new virus appears in the world, we don't know its R value and we don't know how to stop it.
What happens if it just keeps infecting with nothing to stop it?
Hands-on models, sketches, drawings, tables and graphs are all tools of a mathematician.
Population Size = 200
- Enter R = 1. Enter 'go'. Tap F9 until the Yellow cells stop changing to Purple.
**Note: On some keyboards you will need to hold the Fn button whenever you tap F9.**- Check the table to see which week it stopped.
- Count the Purple Squares to know the active cases.
- The F9 action stopped because the pattern is clear already.
Predict the number of weeks to reach 200 active cases. (Hint: Week numbers start at zero. Week**0 <—> 1**Active Case.)
- Choose three (or more) R values. For each one find the week in which the Active Cases reaches 200 people. That means 200 Active Cases.
For each choice,*before you experiment*, predict the number of weeks. Record your predictions and explorations.
- Change the population size to your own choice. The maximum is 1000.
Check that the correct number of boxes have turned yellow. - Predict the week in which the Active Cases will reach (or be greater than) your population size. Record the week.
- Enter R = 1. Enter 'go'.
Tap F9 and watch the Active Cases box until the week it reaches, or passes, your population size. Record the week. - Choose three (or more) R values. For each one find the week in which the Active Cases reach (or are greater than) your population.
For each choice,*before you experiment*, predict the number of weeks. Record your predictions and explorations.
The human population of the earth is 7·8 billion. - Suppose R = 1·5.
*Predict*and record the week in which the earth's population will be reached. Do you think the spreadsheet could go that far? Enter R = 1·5, try it out.Keep watching the Active Cases box above the grid so you know when 7,800,000,000 is getting close. (Something special happens when you reach or go greater than the Earth's Population.)Record the result and comment.
- Predict for R = 2, 3, 4, 5, 6, then explore to find the week in which the Active Cases reach the population of the earth.
Record your predictions and explorations in a table. - Imagine a new virus has appeared.
*Remember, when a new virus appears, we don't know its R value*. Use your data to prepare a brief report to a politician to explain what might happen if nothing is done to battle the virus.
Your report is called a 'worst case scenario'. For each R value in your report you are showing the worst that could happen.
Discuss with someone at home, or class mates, things about the world that would make it harder for the virus to spread to everywhere. ## Exploration 2: Recovery
Open this Excel spreadsheet again and choose View / Full Screen.
- For each one make a table that compares your previous numbers (no recovery) to these numbers (recovery).
- Comment on the effect of including recovery in the model.
## Exploration 3: Changing R
When it started it was just one overseas traveller and no one was too worried. We didn't know then that it had R=3. Then in Week 4 (only one month) there were 81 New Cases and 108 Active Cases altogether. We had started getting a bit worried and washing our hands more and doing social distancing, but it wasn't enough. We were asked to stay and home and work from home and even not go to school.
The next section uses actual Victorian data to show that R really did change.
IF a vaccination is found to fight the virus, the vaccine will be waiting in people's bodies to attack the virus when it arrives.
Open this Excel spreadsheet again and choose View / Full Screen. This example will help you plan your investigation. Open Option 4. - Click on the graph and change the border to fit your screen.
- In Option 4 you can change the R value the same way as Option 3.
- You can also change the percentage of the population who get vaccinated.
- Start with R=3 and 0% vaccinated.
- Spread the virus to Week 4.
- Record the New Cases and Active Cases.
- Vaccinate 20% of the population. That means 1 person in every 5 is vaccinated.
- Spread the virus to Week 20.
- Record the New Cases and Active Cases now.
- Delete 'go'.
Open Option 5. - Click on the graph and change the border to fit your screen.
- In Option 5 you can change the R and the percentage the same as Option 4.
- Start with R=2 and 0% vaccinated.
- Spread the virus to Week 4.
- Click on the graph and record the New Cases and Active Cases.
They should be the same as your Option 4 experiment. - Vaccinate 1 person in every 5.
- STOP and look at the dotted lines.
They show you what would have happened in Week 5 if no vaccine was available. - Spread the virus to Week 20.
- Click on the graph and record the New Cases and Active Cases now.
They should be the same as your Option 4 experiment (30,114 and 48,935). That is still way, way too many cases, but the dotted lines tell you 20% vaccination has made a difference. - Record the values for the dotted lines and explain how much difference 20% vaccination has made to an R=2 virus that spreads for four weeks before vaccination is available. (See below in Answers & Discussion to check your work.)
Now design your own experiments to gather information for the reports you have been asked to prepare. ## Just Before You FinishThe main purpose of this activity is to allow you to do the same work as professional mathematicians do when there is a serious virus outbreak.You have been learning to work like a mathematician. - Print this Working Like A Mathematician page.
- Put a tick beside anything you have done in this activity that is on this list.
- In your journal, finish this paragraph:
*I was working like a mathematician when I...* - Also in your journal answer this question:
*What do you know now that you didn't know when you started this investigation?*
## Answers & Discussion
Maths At Home is a division of Mathematics Centre |