Herd Immunity

[Tabitha8]

A simple title for what I think is probably a complex subject.

If we have herd immunity to an illness as a result of vaccinating our children, how is that maintained given that we don't vaccinate ourselves, the grandparents, our neighbours, etc?

Yes, leBFG. Because then you can say that it doesn't matter for others if you don't vaccinate your children since we're not at 'the threshold'. It's a guilt assuaging thing imo. Anti-vaxers like to believe that vaccine induced herd immunity is a myth (but love how it works no problem with CP vaccination because the impact of herd immunity with CP is to increase incidence of shingles)

There are different definitions of herd immunity, I've linked to/quoted some of them but none of them allow this idea of there being 'a little herd immunity'. The most popular/widely accepted meaning on this thread seems to be that when a certain proportion of the population are immune, the disease becomes stable within the population. The thing that some of you seem to be unable to accept is that this is a mathematical concept. When the threshold is reached, there is herd immunity, if it is not, then there is not. You can talk about reducing susceptibles all you want but you can't define it as 'herd immunity' until you reach that threshold. R

bm, I'm lost as to how you find such simple concepts so confusing. Here's your first quote, which accurately explains that

"The term herd immunity has been used by various authors to conform to different definitions..... We propose that it should have precise meaning ...: "the proportion of subjects with immunity in a given population"

It is very clear, and totally unarguable, that the proportion of immune subjects in a population can be anything between zero and one. It can be 'little', large or anything in between..

Yes, that was their proposed definition and only one example given. That is not the context in which people are using it on this thread. In that example, the definition they used to describe what most people are talking about on this thread is 'herd effect'.

Term* they use to describe

Well. here's another:
definition of herd immunity

Personally, this definition and the one in your link is EXACTLY what I am referring to. I know you don't like it because you can no longer say 'Oh, there's no such thing as herd immunity below x% immunized' but that shouldn't be the reason for choosing a certain definition.

From your link:

"in which a significant proportion of the individuals are immune"

you said none of the definitions you had linked to allowed for herd immunity to be small. This was an untrue statement.

If a small proportion of people are immune, i.e. herd immunity is small, the herd immunity effect, often measured as the immunity-related reduction in the speed of spread of the disease, relative to the speed of spread in a naive population, will also be small. It is clear, and totally unarguable that the reduction in speed of spread of a disease due to immunity may be small, large, or anywhere in between.

You really are on a hiding to nothing here bm. Come back when you've got the maths straight.

As I said, BM, I'd guess that the relationship is S shaped (a logistic function). So at very low levels of vaccination I wouldn't expect the effect to be significant (similarly the marginal effect at very high levels would be small). As the levels increase, the effect on transmission increases disproportionately to the middle of the curve where it starts to decrease.

I agree with Jo, BM. Either you're wilfully not understanding or you need to brush up on your maths (especially probability functions).

"'The most popular/widely accepted meaning on this thread seems to be that when a certain proportion of the population are immune, the disease becomes stable within the population." I completely disagree that the thread has agreed to this defintion of herd immunity as it is clearly referring to HERD IMMUNITY THRESHOLD

"When the threshold is reached, there is herd immunity" - you are talking about the herd immunity EFFECT here. The threshold only tells us about whether a disease spreads or not.

Here's a simple example. Half of people in a population are immune to an infectious disease. Of the 10 people you mix with 5 are immune and 5 are potential sources of infection. If all 10 were not immune, every encounter with an ill friend could render you ill. When herd immunity is at 50%, you are exposing yourself to less ill people. You may avoid ever becoming ill, though your chances are much less if 90% of people you encounter are immune. This is why the EFFECT of herd immunity is still measurable under threshold levels.

As Elaine says, the particular profile will vary depending on many factors I can't think of (how contagious/rate of transmission of the disease is a pretty obvious one).

Well Jo, earlier you argued that herd immunity only had one meaning. Which one were you thinking of?

I said none of them allowed for there to be ' a little herd immunity'. In your example, the herd immunity effect can not be small. It either exists or it doesn't - as the math shows.

Are you seriously trying to argue the the statement R

No BFG, the herd immunity threshold is the percentage of the population that need to be immune in order for the disease to become stable in the community.

Spot the difference:

percentage of the population that need to be immune in order for the disease to become stable in the community

a certain proportion of the population are immune, the disease becomes stable within the population

You left out a bit from the second quote leBFG - 'when a
certain proportion of the population are immune, the disease becomes stable within the population.' The 'certain proportion' refers to the herd immunity threshold, the state of being at or above that threshold is herd immunity/herd effect.

The herd immunity effect is the immunity-related reduction in R. Consider a case where R is 3 in a naive population (zero immunity), and 2.9 in a population with 10% immunity. The herd immunity effect, R reduced from 3 to 2.9, is small. This is very clear and totally irrefutable.

At some level of population immunity, the herd immunity effect is sufficient that R falls to 1. This level is called the herd immunity threshold.

Given the sheer volume of total bollocks you've disseminated on vaccine threads, I'm finding it not inconsiderably entertaining to find you demonstrably and unambiguously flailing around, out of your intellectual depth, on a topic core to understanding vaccination.

Oh come on, I'm the one bumbling about on this topic, not Bumbley hence why I started the thread.

I really have got to stop as this is taking up so much time with so little reward!

BUt here is another description of the process
basic epidemic theory

They define herd immunity as simply that 'Vaccinating an individual indirectly
reduces the risk of infection of this individual?s contacts'

The 'threshold' they call 'Critical'vaccination'coverage'. ie The minimal proportion
needed to be vaccinated in order to prevent an epidemic (ie bring R down to below 1)

BM Slide 10 models for you the relationship between vaccination coverage, R0 and infection attack rates. As you can see, there is no magic point where the number of immune suddenly matters. It's simply that there is a point where an epidemic can be sustained and one where it will die out.

A bit like population growth - when each woman replaces herself with more daughters, a population will grow. When each woman replaces herself with fewer than one daughters (on average) a population will die out. A population is either growing or it's not. But the RATE of growth (or decline) is very important. It matters a lot if your fertility rate is 1 child per woman or 2 children per woman even though both are below replacement levels and the population is declining and both will eventually die out. It's the amount of time it takes which is also important.

Jo, Herd effect is the reduction of disease in the unimmunised population as a result of immunising a proportion of the population.

R is the effective reproductive rate. It is the basic reproductive rate (R0) discounted by the proportion of the population that is susceptible (x). Eg. If R0 is 10 but only half the population are susceptible (x =0.5) then R = 5 (10x0.5). In order for the disease to become stable in the community then R needs to = 1 (if it is < 1 then the disease will die out).

The 'immunity-related reduction' in the above example is x. x is not the herd effect. X is the proportion of the population who are not immune.

Elaine, you find one line on one slide from one presentation by one author that says that and that negates all the other definitions/links that have been given here? The 'magic point' is the herd immunity threshold ie the point where the disease will become stable or, if the threshold is exceeded, will die out.

Actually their definition fits in nicely with what everyone else is saying....apart from you.

What is wrong with that definition apart from the fact that you don't like it?

You're also wrong speaking about a disease being 'stable'. A disease will only be stable when R = 1 exactly. In the same way that a population will only be stable when the net reproduction rate = 1 (ie taking into account mortality, each woman produces one daughter on average). When R > 1, a disease will spread - ie an epidemic. When R < 1, a disease will die out. If you can sustain R < 1 through reducing the number of susceptibles in a sustained manner, you can eradicate a disease in a population. This is the herd immunity threshold. R will fluctuate as the balance between susceptibles/infected/removes fluctuates.

However, the point I am making which you are failing to address either because you don't understand or because it doesn't fit with your world view is that below that threshold, it matters A LOT to disease transmission if R = 1.1 or R = 3. If by vaccinating, you can reduce R from 3 to 1.1, even if you are above the threshold (ie a disease will spread), you will have longer between epidemics and the severity of an epidemic will be reduced. This is shown in slide 10 of the presentation I linked to. Therefore, any non immune individual's probability of contracting a disease will be affected by the number of vaccinated people in the population, even if the number of immune people is not sufficient to stop a disease spreading.

Whooping cough is a good case in point. In other words, any one individual choosing not to vaccinate their children has an impact on the probability of other children getting the disease in question even if vaccination levels are not high enough to completely prevent outbreaks. I know you don't like this fact and this is why you are pretending that it's not true and using a rather frustrating smoke and mirrors technique around definitions - but you unfortunately you can't argue with mathematical realities.

This thread reminds me of that scene from Monty Python's "The Search for the Holy Grail" with the Black Knight who refuses to stop fighting even when he's had all his limbs cut off!

"The 'immunity-related reduction' in the above example is x. x is not the herd effect. X is the proportion of the population who are not immune."

It's no mean feat to contradict yourself within so few words. x can not simultaneously be both the reduction in R (statement 1) and the proportion of unimmune people (statement 3).

The herd immunity effect in my example is [R(0)-R(0.1)]/R(0) = [3.0-2.9]/3.0 = 3%.

Thanks for the black knight Elaine. It's good to start the day with a chuckle.

So, bumblymummy- should children be vaccinated against polio or not? Yes or no.

Elaine, it does not fit in with most of the other definitions that have been posted. Can you really not see that?

Wrt herd immunity threshold. If the threshold is reached then the disease becomes stable (R=1) , if the threshold is exceeded then the disease will die out. (R

Jo, note the quote marks.

Also, what are you doing with your calculations?

In your example, if R = 3 in a population with no immune then R0 = 3.

If 10% are immune then the fraction of the population who are susceptible( x) is 0.9.

R = R0x so, in your example, R = 2.7 not 2.9.

Maybe not so 'clear and totally irrefutable' as you thought...

The herd immunity threshold in your example would be 66%. Ie 66% of the population would need to be immune for the disease to become stable in the community. If that threshold was exceeded then the disease would die out.

What would be the difference on disease transmission between an R of 1.1 and an R of 3?

Actually your calculation above just makes the point further! You have further reduced R by immunising.

What is the effect on disease transmission of reducing R? does it matter it R = 1.1 or if R =3? You keep on avoiding this question and just saying that a disease will die out if R < 1. We know that, there is no disagreement on this issue.