One of the topics we've recently been covering in the final year is how infectious diseases can spread through a population and how they may be controlled using vaccination.
By separating a population into different categories, for example, people who are susceptible to a disease, people who are currently infected by the disease, and people who have recovered and gained immunity, we have been able to write down a set of equations that explain how a person can progress through those different categories, depending on how contagious the disease is and how long a person remains infectious for once they have the disease.
The equations themselves are systems of differential equations and extend on material encountered in C4 at A-level mathematics.
By analysing the equations using a variety of pencil-and-paper techniques, we have been able to show that if some the population can be vaccinated, there will be fewer people in the susceptible category (they will instead have immunity) and the ability of the disease to spread through the population is compromised.
Indeed, if enough people are vaccinated (and note this is not everyone) then the disease cannot spread through the population.
One of the specific examples we have looked at is measles and we have seen that if approximately 96% of the populaton can be vaccinated, then that disease can be eradicated.