The Herd

The Wexford Science Café is still lumbering along after three years of monthly meetings. Somehow, the mantle of Convener and Master of the Rolls fell upon my shoulders and I haven't been able, like St Martin, to find a beggar with whom to share it. There are 40+ people on The Rolls but, even with a following wind, no more than 10 people ever turn up and nobody, ever, volunteers to think of a topic and prepare 5 minutes of material to launch discussion. At my pleading, the suggestion materialised that we have a go at vaccination, but the suggester wasn't able to make an appearance that day. I was okay with that because I had a mass of material loaded up on The Blob about the ethics, epidemiology and economics EEE of Gardasil the controversial vaccine against Human Papilloma Virus HPV and by extension against cervical cancer. Here are those links H - P - V - Splashback. I clagged them altogether into a 5,000 word briefing document and sent that out to The Roll as preparatory homework.  But then, dang-and-blast-it, on the night I was caught up on the farm waiting for someone to come and take two bales of last year's haylage. I got three other unavoidably delayed apologies and nobody claimed to have turned up so I suspect that we can do Vaccination for the April meeting and nobody will complain.

One of the compelling reasons for choking back your anxiety about side-effects and getting your healthy, well-fed, warm-housed, walking, middle-class child vaccinated is the idea about Herd Immunity. If enough susceptible people become unable to propagate the pathogenic virus because they have been vaccinated then the virus doesn't propagate through the population. This means that the poor, the dispossessed, the very young and the immuno-compromised don't get exposed to that virus and so do not die, . . .or survive deaf, blind, brain-damaged or heart-damaged. Go on Rich Reader, take one for the team in a community spirited way: you have nothing to lose but your firstborn.

In the back of my 'mind' I've always know that the epidemiology of vaccination is different for each pathogen. Some diseases are really difficult to catch (Leprosy) while others propagate easily (chicken
pox). Then I came across this really handy document written by Patrick Honner a New York high-school teacher and jobbing quant. It explains the maths of herd immunity. You should read it.

The point Honner makes is that we'll all be fine if each infected person transmits the lurgy to one other person: that's linear growth. If each one infects 2 other people, you have exponential growth because those two pass it to 4 those four to 8 and after 10 rounds of replication you have 1024 people down sick - a kilobug you might call it. If we can interrupt or slow down the propagation to one-a-time after ten rounds only 10 people have been affected. There are two aspects of the life-cycle of the pathogen that are relevant 1) how easy it is to catch and b) how long is the infectious period.  These can be conflated into a single statistic the 'basic reproductive ratio' R₀ which varies for each disease. Measles [tiny case shown R above] is usually reported as top of the list:

Measles	Airborne	15
Diphtheria	Saliva	7
Smallpox	Cough	6
Polio	Fecal-oral	6
Rubella	Cough	6
Mumps	Cough	5
HIV/AIDS	Sex	3
Pertussis	Cough	5
SARS	Cough	3
1918Flu	Cough	2
Ebola	Bodily fluids	2

Honner goes on to explain the very simple math to convert these R₀ figures to a Herd Immunity Threshold HIT which is the % of the population that needs to be vaccinated to knock a given disease on the head. The HIT is inversely proportional to the R₀ and equals about 90% for measles but only 50% for pandemic 'flu. One problem is that measles is communicable for 4 days before first symptoms appear, so it's roared through Miss Kehoe's First Class before anyone knows it's in town. That's one reason why the HSE really pushes out the flu vaccination programme each Winter because you don't need to get everyone on board to achieve significant results for the population 50% will do and that's achievable. It is also the reason the WHO was able to bring Ebola under control at all at all. A ripping through the kids disease like measles requires extra-ordinary levels of compliance to achieve the HIT. Back in the 1950s and 1960s with polio, leg-braces and iron-lungs really fresh in parents' minds, several Western countries were able to achieve those necessary compliance numbers or close to them. Not any more. Parents tend to be young adults who in the core of their being think that they and their loved ones are immortal, so they don't buy into actively preventing infectious diseases. They don't buy into preparing for a long number of years after retirement either - but that's another story.
If you're a teacher this worksheet may be useful.