Life saving maths: How does vaccination work?

Format: Lessons
Language/s: English
Resource Link: View the Lesson
Short Description:

Vaccinating a large enough proportion of children means everyone is protected, including those who can't be vaccinated.

Key Concepts addressed:


Provided a large enough proportion of children are vaccinated, however, everyone is protected – including those who can’t be vaccinated.

In 1998, Andrew Wakefield published an article in The Lancet, claiming that he had discovered a link between the MMR vaccine (for measles, mumps and rubella) and autism. Many parents decided not to have their children vaccinated, despite the scientific consensus that there is no evidence of such a link. As a result, the number of cases of measles and mumps rose sharply.

It has never been necessary for 100% of children to be vaccinated, and there are some for whom it is definitely not in their best interests, such as children with any disease that affects their immune system, and those who have received a transplanted organ. This is known as herd immunity.

But how does this work? How do we know what the rate should be? For measles, it is 95% – how do doctors know that?

Mathematical modelling provides the answer, helping us to understand how epidemics spread and how vaccination prevents the spread of disease. In the video clips in this pack, Dr Julia Gog and Dr Andrew Conlan, of the University of Cambridge, explain using simple models. The accompanying activities will help students to understand how these models work, and how mathematicians can help policy makers to make sensible decisions.