infecting people in a population,

one of the things we really want to know

is whether it's going to continue to spread

and infect more and more people,

or whether it's eventually going to die out

Some diseases like measles are highly infectious

In a fully susceptible population, each measles case

will on average infect about 16 to 18 additional people

Something like flu, however, is less transmissible

each case, on average, would infect between 2 to 3 people

The number of cases that each infectious person generates

can vary for different diseases

and we call this number the Basic Reproduction Number,

or R0 for short

R0 doesn't depend on how severe the symptoms are,

rather it's a measure of how transmissible the infection is

and as a result we can use it to work out

what's required to stop an epidemic

One of the ways we can stop epidemics is using vaccination

Now you might think that to stop a disease

you need to vaccinate the entire population

but actually this isn't the case

Of course if you vaccinate someone

it protects them, and stops them from getting infected

But because people who are vaccinated can't pass it on,

vaccination also stops the chains of transmission

and that means that this can create a protective barrier

which actually stops the epidemic

spreading within a population

Say the basic reproduction number of an infection is 2

This means that in a fully susceptible population,

each infected person will on average

give the disease to 2 other people

But if 50% of the population are vaccinated,

each infectious person on average

will only be able to give it to 1 of these 2 people

and this means that the epidemic

wouldn't be expected to grow over time

This is known as herd immunity

Herd immunity means that long as a certain proportion

of the population is vaccinated,

the disease won't be able to transmit within that population

We've seen that if the basic reproduction number, R0, is 2,

we need to vaccinate half the population

to stop disease transmission

By the same logic, if R0 is 3,

we need to vaccinate two-thirds of the population

If we keep going, for highly infectious diseases like measles,

we need to vaccinate 17 out of every 18 people

or 94% of the population to stop transmission

Herd immunity is especially useful for

protecting members of the population

who can't be vaccinated

perhaps because they're too old, too young, or have weak immune systems

If they're surrounded by people who have received the vaccine

then that can protect them from infection

If however people forego vaccination

then the herd can no longer protect these people

This means that the population as a whole

can be vulnerable to outbreaks

So far, we've been talking about averages,

one of the big challenges in my work

is incorporating some of the complexities of reality

into these mathematical models

Vaccines are an incredibly powerful public health tool

and the best way to protect populations against disease

is to make sure as many people are vaccinated as possible

so we don't run the risk of slipping below

this vaccine threshold for herd immunity