It's been 2 years since I posted this blog, and it's still one of my favourites.
Here's a tweetorial on herd immunity, and why it's pretty cool #VaccinesWorkhttps://medium.com/@gidmk/herd-immunity-is-pretty-cool-adbc52630f9f …
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Here are some common R0s for various vaccine-preventable diseases, as per the CDC You can see why measles is such a problem!pic.twitter.com/ypkYMrciAp
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So this is the reproduction rate of the disease in an entirely vulnerable population. It's pretty simple - you look at each person, check their contacts - people they interacted with while infectious - and see how many get the disease What happens if people are immune?
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Here's where the maths comes in. Now, immunity can be conferred by vaccines, but it doesn't HAVE to be. Even without vaccines you start seeing herd immunity once 90%+ of the population has been infected
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(The downside to this, of course, is that most people get sick and some die from the disease to earn that immunity, whereas vaccines are much safer)
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More The EFFECTIVE reproduction rate (R) is calculated based on the R0 Mathematically, it is: R0*y = R Where y is the proportion of the population susceptible to the disease
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Based on the table above, what's the R for measles in a population with 75% vaccination rates?
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Here's a more difficult question - based on the equation for R, what is the formula to work out the % for herd immunity (HI)?
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This is more complex because you have to think about what herd immunity really means Herd immunity means that each person passes on the disease to fewer than 1 person (on average), so the disease eventually peters out
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What this means, in technical terms, is that R<1 I.e. the effective reproduction rate in the population is less than 1
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Mathematically, this gives us the minimum threshold for herd immunity as: R0*(1-HI) = 1 Where R = 1 and R0 is calculated based on the disease Turning this around, we get: HI =1-(1/RO)
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So to work out the threshold for herd immunity, we just have to solve this for each disease! Pretty cool, huh?
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What's the herd immunity threshold for mumps, based on this formula?
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Completing the formula, we get: HI = 1-(1/4) to 1-(1/7) = .75-.86 = 75-86%
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What this means is that we have to vaccinate 75-86% of the population to reach the threshold for herd immunity for mumps
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The more infectious the disease, the more you have to vaccinate Measles can live for hours, even days, outside the body, and has an R0 of >12, which means that we need to vaccinate 95% of the population to be sure it won't spread
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Smallpox only has an R0 of 7, which means that we only had to vaccinate ~85% of people to eliminate the disease
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And that's it. That's how herd immunity works Simple, easy, incredibly, wonderfully powerfulpic.twitter.com/GywhQILLPQ
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People do still get these diseases. No vaccine is 100% effective - although many are close to that - so vaccination rates often have to be higher than even the theoretical herd immunity threshold
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There are also a lot of people who have been scared away from vaccination by anti-vaccine activists who spread fear about lifesaving medical interventions
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But we know that vaccinations WORK Australia has now eliminated endemic measles and rubella, and almost entirely eliminated many other infectious diseases, with some of the highest vaccination rates in the world
#VaccinesWorkpic.twitter.com/MdFUNBp6U7
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So get your vaccines They will not only stop YOU from getting sick, they'll also stop you from passing diseases onto more vulnerable people like babies and immunocompromised people
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And the next time someone says "herd immunity is a myth!", feel free to reference this thread and/or blog Herd immunity is simple maths, nothing more, nothing less
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End of conversation
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