Herd immunity is a mathematical function of R0, the basic reproduction rate.
The higher the reproduction rate, the higher the percent of the population which must be immunized (by vaccine or previous infection)
Herd immunity threshold = 1 - (1 / R0)
If R0=2, you need to vaccinate 1 - (1/2) = 50% of the population. Think of the flu.
If R0=5, you need 1 - (1/5) = 80% of the population vaccinated. Think polio.
Measles famously has an R0 of 12+.
To reach herd immunity with measles, 1 - (1/12) = 91% at least of the population needs to be vaccinated.
The percent of the population necessary to be immunized, raises as the disease's infectiousness increases.
R0 is not an intrinsic property of a disease, it's an estimate based on mathematical models with assumptions.
Polio has an R0 of 5-7 assuming no one deliberately shits into the water. If they do, it'd be higher than this.
If everyone takes proper precautions, it'd be lower.
The *actual* R0 of a pathogen can vary wildly compared to these models.
Flu may have an R0 of 1.3, but if everyone coughs into each other's mouths, it'll be much higher.
It depends on environment and behaviour.
What this means is that if you model a disease to have an R0 of 5, you will need to vaccinate 80% of the population.
If you alter the environment and behaviour of people to encourage spread, you increase its R0. And you will have to vaccinate a greater percent.
If you alter the environmental conditions and behavior to minimize the spread, you reduce the R0 and the percent of population to be vaccinated, decreases.
If you take no measures against measles, you need to vaccinate against an R0=12-18 disease. You will need to vaccinate at least 91% of the population.
Every effective measure you take to limit spread, increases the bang for the buck of the vaccine.
For the flu, with an R0 of 1.3, you reach herd immunity by vaccinating 1 - (1/1.3) = 23% of the population.
You don't *need* to vaccinate 91% of the population against the flu the way you would with measles.
And if your myriad of various safety measures somehow amazingly reduced the spread of measles to the level of flu, you'd find yourself reaching herd immunity much quicker.
Relying on a vaccine *without* otherwise attempting to limit spread, means you're using that estimated R0, at least. It may be higher, if you're taking actions which encourage spread.
Suppose you have modelled a disease to have an R0 of 10, meaning you're gonna have to vaccinate 1 - (1/10)= 90% of the population.
The more measures you take to limit spread, the lower that herd immunity threshold gets. The vaccine becomes more useful the better you are at this.
If you don't limit the spread, and actually do things to encourage a higher R0, it will be even harder to reach herd immunity.
You *want* there to be multiple simultaneous policies in place to reduce R0. It means herd immunity becomes easier to achieve.
Anosognosiogenesis
@pookleblinky
·
Jan 10, 2022
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