21. The Vaccination Program Problem

26 Sep
maths with zombies

…because everything’s better with zombies!

Two months ago, a frightening new disease emerged out of nowhere and killed several hundred people in a remote farming community before it was successfully brought under control by the army. Based on the testimony of the few survivors, this disease caused those infected with it to violently attack and bite anyone they could get their hands on. Those who were bitten soon started doing the same and it’s no surprise that this new disease has been dubbed ‘The Zombie Disease’ by news reporters. You’re worried that if a similar outbreak happened in a more heavily populated area, the disease could quickly sweep across the whole country or maybe even the world, before it could be brought under control, and this could bring humanity to an abrupt end.

After many weeks of hard work, you’ve created a virus against this new disease and you’ve calculated that to be effective at stopping any further outbreaks getting out of hand and turning into a full-blown zombie apocalypse, you need to make sure that at least 95% of the population is vaccinated. It takes 6 minutes to give someone a shot and you have a team of 2,500 trained health professionals to administer them, each of whom can work for 16 hours a day. To the nearest whole day, how long will it take to vaccinate enough people in the USA (assuming a population of 250 million) to prevent a zombie apocalypse happening there?

A: 297 days.

B: 396 days.

c: 475 days.

D: 594 days.

Scroll down to see the right answer…

What answer did you get?

A: You’re way off there! You’d twice as many health professionals to get 95% of the population vaccinated in that amount of time.

B: Your team could only get it done that fast if they worked 24 hours a day, and there’s no way they could do that for very long.

C: Something’s gone with your calculations there, or are you only going to give your staff four hours off a night? If they don’t get enough rest they’ll end up making mistakes and you’ll miss your target of having 95% of the population vaccinated.

D: Spot on, but if you’re going to get everyone vaccinated before there’s another outbreak, you’d better get started as soon as possible.

How to work it out: For the vaccination program to be successful, you need to vaccinate 95% of the population, so the first thing you need to do is work out how many people that is. This is done by multiplying 250 million (the total population size) by 0.95 (95% expressed as a decimal fraction). This tells you you’ll need to vaccinate 237.5 million people. Next, you need to work out how long it will take to vaccinate this many people. It takes 6 minutes to administer each vaccine, so the total time is 6 times the number of people to be vaccinated (237.5 million), which is a staggering 1,425 million minutes. However, this isn’t the actual time it will take, because you have 2,500 all of whom can be working at the same time. To work out the actual time, you need to divide the 1,425 million minutes by the number of workers you have on your team (2,500), and that gives you an actual time of 570,000 minutes or, if we divide it by 60 (the number of minutes in an hour), 9,500 hours. Each worker can only work 16 hours a day, so to get the actual number of days it will take, you will need to divide the number of hours required (9,500) by the length of each person’s working day (16 hours), this gives you the required length of your vaccination program in days, which is 593 and three-quarter days, or, to round it up to the nearest whole day, 594 days. As you can see, vaccinating a population against a disease can take a very long time!

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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