Question: How do mathemathical equations help to find out about how diseases spread?

Leo Beacroft answered on 8 Jun 2018:

This is a good question, as it’s not obvious how maths relates to diseases spreading. Scientists like myself can use equations to describe how a disease spreads and this can help to predict how it might spread in the future. Let’s use a simple example. Imagine we want to know how many people will have flu at the end of next week. We could write this as an equation.

T = a + n – r
T is the total number infected at the end of one week
a is the number already infected at the start of the week
n is the number of new infections during the week
r is the number of people who recover during the week, that’s people who were infected but get better.

What’s interesting is that all of these things are related to each other. If “a” is large, then there are a lot of infected people to spread the flu so “n” will be large too. We can build this into our equation to make it more complicated. We can go further; we can think about how many people each person with flu is likely to pass the disease on to. We know flu is spread through water droplets in the air, often through coughs and sneezes. The number of people that a person spreads the disease to depends on how many people they come into contact with. If someone is ill and they stay at home by themselves, they might not spread it to anyone, but if they go to work in a busy office, or school, they could spread it to 20, 30 or more people. When scientists are writing equations, we try to think about these different types of people, how many people will stay at home? How many people will come into contact a few people, how many will come into contact with lots of people? Including all of these things in equations might help to make better predictions about how the disease will spread.

Thanks for your question, does that make sense? Let me know if you have any more questions 🙂