4. The Viral Spread Problem

9 May
maths with zombies

…because everything’s better with zombies!

There’s a virus turning people into zombies who attack the living and never die. No one knows where it came from but the first person (known as ‘patient zero’ by those who study how diseases spread) was an archaeologist who’d just discovered an ancient tomb so it might have come from there. The virus is spread when infected people bite someone who’s uninfected. If each zombie bites an average of three uninfected people each day, how long will it take before the entire human population of the planet (which for this problem will be taken as 7 billion people) are turned into shambling undead flesh-munchers?

A: 167 days (almost 6 months).

B: 53 days (just under 8 weeks).

C: 17 days (just over two week).

D: 6 days (less than a week).

Scroll down to see the right answer…

What answer did you get?

A: You’re way off! You’ll have no chance of stopping an outbreak if you can’t work out how fast it will spread.

B: You’re closer but you’re still dangerously under-estimating how fast the disease will spread.

C: Spot on! Now you know exactly how long it will take before humanity is gone.

D: You’re a pessimist aren’t you? The last human won’t become infected for another 11 days.

How to work it out:The simplest way to work it out is to calculate the number of people infected at the end of each day given the number of people infected at the start and the average number of people they will bite, and so infect. For day one, there will be one person infected at the start of the day (the unfortunate archaeologist) and he will infect three people by biting them. This means that at the end of the day there will be 4 zombies (1 + 3 = 4). Day two starts with 4 infected people, each of which will bite and infect three people. That’s a total of 12 people (4 * 3 = 12). At the end of day two there will be a total of 16 zombies (4 + 12 = 16). If we carry this on, we’ll find that at the end of day three there will be 64 zombies, 256 at the end of day 4 and so on, until at the start of day 17 there will be 4,294,967,296 zombies, and since there’s only 7 billion people on the planet, they will run out of uninfected people to bite somewhere around lunch time.

Note: While the problems provided here are copyright of Maths With Zombies, if you are a teacher, you can use any of these problems for free in your classes – but please credit Maths With Zombies as the original source (e.g. Downloaded from MathsWithZombies.wordpress.com). You can download a PDF handout of this problem from here. If you do use this problem in a class, please post a comment here to let me know how you used it and how it was received by your students. These problems cannot be used for any commercial purpose without express written permission.

From the author of For Those In Peril On The Sea, a tale of post-apocalyptic survival in a world where zombie-like infected rule the land and all the last few human survivors can do is stay on their boats and try to survive. Now available in print and as a Kindle ebook. Click here or visit www.forthoseinperil.net to find out more. To download a preview of the first three chapters, click here.

To read the Foreword Clarion Review of For Those In Peril On The Sea (where it scored five stars out of five) click here.


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