When a new disease emerges and starts
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