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?

Ginny, 0.02% of those who contract polio.

Widespread tetanus?

Wrt flying bringing in lots of illness. There are plenty of diseases that are rife In other countries that we don't vaccinate against. Do you worry about them being brought in?

I wasn't panicking about swine flu. Tbh I think the ones who were panicking are the ones who are always looking for a science 'fix' to everything rather than actually looking at the disease itself and the likelihood of them actually getting sick and dying from it.

Also Math, I'm pretty sure that no diseases have a threshold of 0.3%

I think, BM, to have significant herd immunity, you would need a significant proportion of the population to be immune.

As I said above, given the exponential nature of disease transmission, I'm guessing that the function of herd immunity for a percent immune would be a S shaped sigmoid function. This means that the effect on herd immunity at low levels of immune in the population would be low and the increase on herd immunity of increasing the proportion immune would be disproportionately low. The effect in the middle of the curve would be greatest but the actual curve would vary according to the disease parameters even if the general shape of the relationship remains the same.

But I should say that I don't really know. I'm just looking at what would result from the epidemic theory model. If you know better, I'd be more than happy to stand corrected. It doesn't really matter since most routine vaccinations lead to significant levels of immunity within the population even if not sufficient to fully prevent outbreaks.

"seeker, I'm still struggling to see what my decisions wrt vacination have to do with this thread."

Because if you express views that go against the currently accepted norms, it's useful to know where you're coming from.

And a person who would be happy for their child to spend the day at school sitting next to someone incubating polio has an unusual mindset or has knowledge the majority doesn't have. And it seems to me entirely reasonable to ask about that. And you seem very cagey about this.

Oh, and I wasn't bothered about swine flu either, because no one in my family fell into any of the vulnerable groups.

A minimum 25% fatality rate in a disease affecting 0.02% of people means, unprevented, 350,000 deaths, based on a UK population of 70,000,000.

70,000,000 x 0.02 x 0.25 = 350,000.

Um, I might be wrong but that doesn't look right to me.

Surely 0.02% of the population would be 0.0002 x 70,000,000? i.e. 14,000 so the death rate would 3,500.

Of course that is a lot of dead people which is awful but if you are looking at risk it makes a big difference.

I can't see where the 0.02% comes from though having scanned the thread back a few days. Was it the conversation on polio?

BM if it is the conversation about polio it is 0.02% of the whole population not 0.02% those who contract the disease.

Good catch BBB. 350,000 people dying in an epidemic is Spanish flu epidemic proportions!

I agree with the sentiments of the post though - any preventable death is a tragedy.

You are right, EB, that any preventable death is a tradgedy so in a sense the figures don't matter. 3,500 is a lot of people in anybody's book so can be justfication enough to think about protecting yourself and your family against a disease.

However, I wouldn't want to see incorrect figures if it means that somebody might see it as an excuse not to face the reality of their decision to vaccinate because it is not that bad after all, or conversely, be frightened into a decision based on an incorrect view of the risk.

Not that this thread is about getting people to vaccinate - I think all minds are firmly made up.

I couldn't agree more regarding good data and statistics.

'Also Math, I'm pretty sure that no diseases have a threshold of 0.3%'
They might have though. It depends on the way the disease is spread and how infectious it is and what population is most at risk. Hence my comments on different diseases having a different threshold.

'seeker, I'm still struggling to see what my decisions wrt vacination have to do with this thread'
To use the example of HIV example again, a decision not to use a condom ever while having sex in bathhouses with gay men would lead to what?
A decision not to vaccinate against Pertussis for instance could lead to infecting someone's baby, with horrible results. Effect of lack of herd immunity in Washington state, USA. Lack of herd immunity happens when PFBism runs amok and many parents decide individually not to vaccinate their little darlings.

'Wrt flying bringing in lots of illness. There are plenty of diseases that are rife In other countries that we don't vaccinate against. Do you worry about them being brought in?'
We have seen HIV hop continents. We have seen H1N1. Containing them is a priority.
We vaccinate against the flu strains that appear elsewhere and we track their progress, a new strain every year. We especially urge the elderly to get the annual flu vaccine.
We don't bother so much with a disease like malaria because we don't have the conditions that would cause widespread malaria here. But measures are taken in parts of the US to spray against mosquitoes and malaria used to kill people in the South. Now that the mosquito has been linked to West Nile Virus, increased attention is paid to the mosquito in North America.
Cholera is a worry even though the water supply is now safe. Cholera can be caught from undercooked seafood from contaminated water and other isolated individual foods that come in contact with a food handler or cultivator carrying the disease, but most cases in the west happen in people who travel without getting vaccinated properly. Cholera is always ready to cause an epidemic if conditions are right.
TB is a constant worry, especially now that there are bacteria resistant strains.

A brief history of brucellosis eradication in Ireland. Brucellosis remained an occupational hazard in Ireland for many in the beef and dairy business until 2009 when Ireland was declared brucellosis free by the EU, but there are still many left with the lingering effects of this disease. In the context of herd immunity (no pun intended) this is an interesting case and a interesting battle that illustrates the effect of a border with different policies on either side (which in turn illustrates the concept of herd immunity).

So bumble, you used a flawed formula to show my calculations were wrong. You agree with me that the formula is flawed (or basic to use your euphemism), and then ask again where I messed up my calculations. I realise this is likely just a stalling tactic.

Can you not see that if your working out was wrong (basic), then so to was your conclusion? You are insisting someone's sums are wrong even after having agreed that your calculator is defective. My calcualtions were 100%. You're grasp of mathematical epidemiology is inadequate.

"'Wrt flying bringing in lots of illness. There are plenty of diseases that are rife In other countries that we don't vaccinate against. Do you worry about them being brought in?"

I'm sorry to bang on about polio, but this is obviously one of the reasons that it's important to vaccinate.

Smallpox has been eradicated, so there is no need to vaccinate against it any more. Polio is getting there, but not there yet.

EB, to have herd immunity ( and here, I'm assuming that you are talking about the protective effect conferred on others) you need to have a significant proportion of the population vaccinated (as per the majority of the definitions posted here). If you don't have a significant proportion vaccinated then you don't have herd immunity ( see diagram I linked to earlier).

BBB, it's a form of polio, bulbar polio, which occurs in 0.02% of polio cases.

math, you don't need to point out that there are different thresholds to me. I posted about it earlier. A disease with a 0.3% threshold would disappear fairly quickly.

The whopping cough epidemic is due to waning immunity from the vaccine. There's a whole thread about it at the moment. Even the CDC recognised that it is not the unvaccinated driving it, the majority of cases are in vaccinated children.

Jo, the formula that I said was basic was for calculating HIT. You calculated R incorrectly. What formula did you use for that?

The relevant question isn't 'are vaccinated people catching wc?'. The vast majority of people are vaccinated after all. The real question is 'are unvaccinated people catching it more than vaccinated?'. If they are, they are spreading it disproportionately.

I only recall my stating 2 values for R for illustrative purposes. Could you quote the bit where I calculated R?

LeBFG, the majority of cases are in the vaccinated according to that link I posted on the other thread. The CDC have accepted that it is the waning immunity from the vaccine that is the cause of the outbreak. Do you disagree with them?

Jo,Do you not think if you are doing something for illustrative purposes that your figures should be correct? Particularly when you go on to say "This is very clear and totally irrefutable'.

The formula isn't 'flawed' btw but it is basic/simple. You said earlier:

"You use this formula to question my calculations. Unfortunately, this formula gives the wrong herd immunity threshold for every single disease in this table."

The formula actually gives the correct threshold for every figure in that table.

For example:

Diptheria R0 = 6-7 (Let's assume 7) Using the formula HIT = 1 -(1/R0)
HIT = 1 - (1/7) HIT = 1 - 0.14 HIT = 0.86 or 86%. If you use R0 = 6 you get 83%. The given threshold in the table you linked to is 85% - the average of the two.

It works for the other ones in the table as well. Why did you think they were wrong? Were you using the formula incorrectly? It is a basic/simple formula. I'm not sure how you went wrong with it.

I'm glad you changed epidemic to outbreak, bm.

Of course the majority of cases are vaccinated, most people are vaccinated after all. To illustrate: more babies die of SIDS when they sleep in the parental bed than on sofas...because that's what most people now do. There is still an a higher proportion of deaths on sofas because this is riskier. What about the proportion of wc in unvaccinated people?

I'm struggling to keep up with these two threads. Please repost the CDC link saying the outbreak (Washington is what we're referring to I think) is caused by waning vaccines so I can read and comment. Thanks.

BFG, there was epidemic declared in Washington state (and Colorado too) but the article I am referring to (not a CDC link) is talking about the outbreak of whooping cough in the US in general.

The other thread isn't too big. I'm sure you can find the information yourself.

Cheers

As I thought, math's link refers to Washington and your statement is about the whole of the States. I've found this - is that the correct one?

An epidemiological model for R(0) minimally needs terms for host density and disease transmission rate. Your formula has no term for disease transmission, and so is flawed. It also ignores the fact that populations are spatially structured and a whole host of other stuff.

Disease transmission is usually dependent on host density, whereas your formula in effect assumes transmission rate is independent of host density, i.e. it ignores the fact that when people are in closer proximity, a disease will pass more easily between people.

I don't see how illustrative figures can be correct or incorrect. They should be illustrative and plausible. Your argument is basically as follows. I said 'consider a case where oranges cost 10p, there's a drought and the price goes up 12p'. Rather than just accept the point that oranges are more expensive after a drought; something which you had previously been denying. You find the simplest economic model known to mankind, which shows that if there was a drought, orange prices would increase 10%. On the basis of this, you say repeatably that my figures are wrong. This allows you to avoid the clear and irrefutable point that vaccinating even a tiny number of people always reduces the rate of spread of a disease. To this extent, people who vaccinate benefit people who don't.

Yes, BFG, that was the one I was talking about. Are you suggesting that waning vaccine immunity didn't have anything to do with the epidemic in Washington?

From Maths link:

"Making things worse, it seems, is an increase in cases among children aged 13-14. Children get a booster shot at age 11-12, but the new outbreak indicates that the effectiveness of the booster may not last very long. The dramatic increase in whooping cough this year also suggests that the bacterium that causes it, Bordetella pertussis, is mutating to make the vaccine less effective. "

It seems to be the author's own opinion that the anti-vaxers are to blame.

Jo, the formula you called 'flawed' is the HIT formula not the formula for R0. You really do seem to have gotten lost here. How do you explain the HIT formula being flawed when it actually calculates the thresholds correctly? (As shown above).

You illustrative figures were incorrect because if you have 10% immunity in the population then R would not be equal to 2.9 as you stated, it would be equal to 2.7, as I've already pointed out. I know you don't want to admit that you made a silly mistake but really?

Herd immunity is not quite 'the protective effect conferred on others'. It is the threshold which once reached means a disease is unlikely to spread. It is an epidemiological concept; the term does not imply that unvaccinated individuals or those with weakened immunity will not catch the disease. If you are not vaccinated you could still catch the disease because of your lifestyle, if the individuals you come in contact with are also unvaccinated and infected, because of the level of infectiousness of the disease, or because of the particular segment of the population a disease tends to strike..

Wrt the allegation that it is waning vaccination effectiveness that causes the rise in whooping cough cases this is amply disproved by the fact that there are pockets of vaccine resistance in the US and these pockets tend to be the places where WC is at its highest levels. Washington, Wisconsin and Montana have the highest rates of vax refusal and WC epidemics. For those cases where waning immunity gives rise to an upsirge in WC, lack of vaccination is also the cause there is a schedule of boosters that everyone is supposed to get, beginning at 11-12 iirc.

Scroll down to table 3 showing exemptions granted to vax requirements by state for religious or philosophical reasons and note the percentage column, third from the right.

States with highest Pertussis rates in the US. It is interesting to note that for those states with a high rate of pertussis that are not also high vax refusers, all are contiguous to states with rates of vax refusal over 1%. In addition, some have a border with Mexico. Some have a high number of immigrants and migrant workers.

Adults need to get a booster because they are not being reexposed frequently as they used to be when diseases were widespread in their wild form. Either you get exposed naturally or you get exposed artificially via vaccine. If you can't get the natural exposure then you should seek out the artificial exposure.

'Historical Comparisons of Morbidity and Mortality for Vaccine-Preventable Diseases in the United States' -- comprehensive overview of the effect of vaccination policy in the US.

I think that's an important point math. It's a probabilistic model so there are no guarantees. It also assumes the population mixes randomly which, as you point out, isn't the case - anti vaxers tend to hang out with one another!

Could somebody explain to me in simple trms for the hard of thinking why we're spending so much time on defining our terms?

I thought "herd immunity" meant that enough people within a community were immune to q particular disease to make it extremely unlikely that a non immune person entering that community would contract whatever it is.

Finally, bm, thanks for being so helpful. I'll return the favour sometime.

I think the CDC comment you made came from page 3:
While some parents around the country have taken a stand against childhood vaccines, the outbreak is not being driven by unvaccinated children, according to the CDC. Most of the illnesses are in vaccinated youngsters, officials said.

From this statement it isn't clear what the 'officials' said and what the CDC said. It appears the statements are linked (i.e. the outbreak is not being driven by unvaccinated children because we see most of the illnesses...in vaccinated youngsters), but in fact they aren't. I would love to see an original CDC statement wrt to this point.

Evidence for waning immunity, bm, comes from the resurgence of wc in the age group 13-14 who exclusively had the new vaccine, not purely from the the fact vaccinated people catch wc (they always have done).

From saintly's CDC link:
Given the high transmissibility of B. pertussis, a proportion of vaccinated persons remains susceptible and can become infected during a pertussis outbreak. Unvaccinated children have at least an eightfold greater risk for pertussis than children fully vaccinated with DTaP (7). However, because in most of the cases the patients were vaccinated, the 4.5% of Washington school children who were exempted from vaccination during 2011?2012 represented only a small proportion of those at risk for pertussis in the state. Although vaccinated children can develop pertussis, they are less infectious, have milder symptoms and shorter illness duration, and are at reduced risk for severe outcomes, including hospitalization (8?10).

The ongoing pertussis epidemic in Washington reflects the evolving epidemiology of pertussis in the United States. Although acellular pertussis vaccines provide excellent short-term protection, early waning of immunity might be contributing to increasing population-level susceptibility

Note the use of healthy scientific skepticism I've highlighted in the text bm.

All-in-all, your bald statement:
The whopping cough epidemic is due to waning immunity from the vaccine... Even the CDC recognised that it is not the unvaccinated driving it, the majority of cases are in vaccinated children. is unsubstantiated.