When a new disease emerges and start infecting people in a population, one of the things we really want to know is whether it’s going to continue to spread, some diseases like measles are highly infectious. In a fully susceptible population each measles case will on average affect about 16 to 18 additional people, some diseases like flu however is less transmissible. Each case on average would infect between two or three 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 Arnold for short. Now Arnold doesn’t depend on how to fear the symptoms, rather it’s a measure of how transmissible the infection is 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 an entire population but actually this isn’t the case, of course if you vaccinate someone it protects them and stop them from getting infected but because people have activated composition, vaccinations also stops the change 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 the infection is 2 this means that in a fully susceptible population, each infected person will on average give the disease to 2 other people with 50 percent the population. Each vacinnated infectious person on average will only be able to give it to one of these 2 people and this means that the epidemic would be expected to grow over time, this is known as herd immunity. Herd immunity means that as long as a certain proportion of the population is vaccinated, the disease won’t be able to transmit within that population.
We need to vaccinate half the population to stop disease transmitted by the same logic, if Arnold is three, 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 about 94% of the population to stop transmission. Herd immunity is especially useful for protecting members of population who can’t be vaccinated perhaps because they’re too old or too young or have vulnerable immune system. If they’re surrounded by people who have received a vaccine, that can protect them from infection. If however people forego vaccination then the herd can no longer protect these people.