Mumps math
Apr. 13th, 2006 10:06 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mmcirvinThe first thing a lot of people probably wondered when hearing about the Iowa mumps outbreak, and especially the number of vaccinated people who got the mumps, was "does this mean the vaccine doesn't work?"
Mark Chu-Carroll and Tara Smith run the numbers. The answer is that the outbreak's consistent with the vaccine working about as well as previously thought. This isn't some kind of super-mumps.
Most of the people who got it were vaccinated. How can this be consistent with the vaccine protecting most of the people who get it? It can be if not many people were unvaccinated in the first place.
Here's an unrealistic toy model even simpler than Tara's. Suppose there are 100 people and 98 of them get their shots. Of the 98, say 90 of them develop antibodies and are immune—an over 90% rate of effectiveness for the vaccine. Then we've got 10 people who are unprotected: 8 who got the vaccine and 2 who didn't. If they all got sick (that's unrealistic virulence, but it shouldn't change the percentages), 80% of the infected would be vaccinated, even though 90+% of the vaccinated are immune.
In reality, the vaccine coverage rate in Iowa is lower than 98%, though different sources of information seem to disagree on the details. But, as the discussion in Mark's comment thread points out, the biggest potential tinderboxes for disease outbreaks—college campuses—also have relatively high vaccine coverage; the people least likely to get vaccinated also tend to be more isolated.
Mark Chu-Carroll and Tara Smith run the numbers. The answer is that the outbreak's consistent with the vaccine working about as well as previously thought. This isn't some kind of super-mumps.
Most of the people who got it were vaccinated. How can this be consistent with the vaccine protecting most of the people who get it? It can be if not many people were unvaccinated in the first place.
Here's an unrealistic toy model even simpler than Tara's. Suppose there are 100 people and 98 of them get their shots. Of the 98, say 90 of them develop antibodies and are immune—an over 90% rate of effectiveness for the vaccine. Then we've got 10 people who are unprotected: 8 who got the vaccine and 2 who didn't. If they all got sick (that's unrealistic virulence, but it shouldn't change the percentages), 80% of the infected would be vaccinated, even though 90+% of the vaccinated are immune.
In reality, the vaccine coverage rate in Iowa is lower than 98%, though different sources of information seem to disagree on the details. But, as the discussion in Mark's comment thread points out, the biggest potential tinderboxes for disease outbreaks—college campuses—also have relatively high vaccine coverage; the people least likely to get vaccinated also tend to be more isolated.
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Date: 2006-04-13 07:20 pm (UTC)Just as a side note, vaccine-resistant strains of pathogens don't tend to be "super"; for the most part, they tend to be pretty seriously weakened compared to the parental strain. That makes sense, because the parental strain is presumably well adapted for its pathogenic lifestyle, and changes in the genome are likely to be away from optimal. That's particularly true because most vaccines either specifically or peripherally target aspects of the pathogen that are particularly important in its lifestyle, so escaping the vaccine-indiced immunity generally means making major changes in a critical aspect of its virulence determinants.
You see this in HIV, it turns out. Some recent studies have tracked HIV over time in series of patients. You can detect changes in the virus in response to the dominant immune response -- as the patient's immune response targets one part of the virus, the virus changes that part and keeps going.
But if that virus now infects a new person (who will respond to different sequences of the virus), the first changes (which are now not necessary) change back, they mutate again until they're close to the concensus sequence of HIV. The changes that the virus underwent to avoid the immune system, therefore, were changes away from general optimality, and given the chance the viruses that mutate back to the starting sequence will rapidly outcompete those immune-selected variants.
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Date: 2006-04-14 04:08 am (UTC)no subject
Date: 2006-04-14 05:49 am (UTC)