Why does a moderate amount of vaccination not majorly cut covid rates?
April 8, 2021 7:54 AM   Subscribe

If the growth is exponential, isn't even a relatively small amount of vaccination going to cut the exponent? Naively I would think that if the R value is, say, 1.1, then vaccination of 30% of the population would drop it to 0.8, which would extinguish the outbreak (or at least decrease it massively). What's going on?

From the slightly increasing U.S. case rates, it's clear that R is greater than 1 in the actual population. So any effect from vaccination is being more than offset by something else. Does anyone have information on what? Is it increased transmissibility, increased risky behavior, are the sub-populations that are unvaccinated that are driving the numbers overall? Happy to read intuitive explanations and scholarly work.
posted by wnissen to Science & Nature (19 answers total) 4 users marked this as a favorite
 
Best answer: I expect your assumption would be true if the distribution of those who are at risk for COVID-19 is uncorrelated with those who receive COVID-19 vaccines. In reality, I expect they are somewhat correlated, with a negative coefficient of correlation - ie, those who are at risk for COVID-19 are less likely to receive COVID-19 vaccines. The groups that are most effected by COVID-19 are low-income non-white people in conservative regions. Correspondingly, those the exact areas that have the lowest vaccination rates.
posted by saeculorum at 8:01 AM on April 8 [18 favorites]


Behavior - those who aren't yet vaccinated are seeing case numbers drop and are going out to eat, traveling, not masking, and doing other stupid things. Those who are fully vaccinated were until more recently the lowest spreaders to begin with. Small changes in risk taking by large numbers of people have a big effect on R so that even if the virus fails to spread through the 30%, it's finding more than enough new hosts anyway among the other 70% who are now making things easier for it by increasing contacts. Also probably variants. Most states that sequence a sample of cases regularly now have a majority of cases from new more contagious strains than the original one.
posted by slow graffiti at 8:11 AM on April 8 [9 favorites]


One factor is that herd immunity does not decrease R value linearly. Look at this simulation: when only a small percentage of people are immune, it has almost no effect on disease spread. Even with 30% immunity (similar to the U.S. right now) the disease can still spread through the entire non-immune population. Only when immunity is at the frequently cited 70%+ level does "herd immunity" really kick in.
posted by steveminutillo at 8:31 AM on April 8 [34 favorites]


This is obviously a really complicated question (and I'm not sure there's any reason why "30% vaccination should drop the R value by 0.3" necessarily works mathematically).

For one thing, R of 1.1 is high and dangerous, but it's not, like, a maximum - early in the pandemic R was over 2 in many places, and there's no inherent reason it couldn't be way higher. R for measles is estimated at 12-18 in an unprotected population. So it could be that vaccination is reducing transmission by a huge amount but the new variants would be absolutely tearing through the population if we weren't taking the measures we're taking.

This article from Zeynep Tufekci from a week or so ago gets into a lot of the details: The Fourth Surge Is Upon Us. This Time, It’s Different. Basically with exponential growth, small changes make a big difference in either direction.
posted by mskyle at 8:31 AM on April 8 [6 favorites]


Other possible factors (this comes under "intuitive explanations"):

1. People of working age and below mostly haven't been vaccinated yet, and they're more likely to be vectors. I'd expect the impact of the first stages of vaccination to be seen in the death rates, not the infection rates.

And also...

2. I'd expect people who've been vaccinated start to behave less cautiously - instead of getting groceries delivered, they start going to the shops themselves; instead of cooking at home, they start going to restaurants; instead of socialising only within their bubble, they start seeing more people. Vaccination doesn't give you 100% protection, so on a population level, I'd expect that sort of behavioural change to have a measurable impact, especially if people change their behaviour prematurely (after just the one jab - or, worse, *immediately* after the first jab rather than giving it the two weeks it needs to take effect).
posted by ManyLeggedCreature at 8:46 AM on April 8 [1 favorite]


Best answer: This article from Zeynep Tufekci from a week or so ago gets into a lot of the details:

She is truly a gem. This article from the fall opened my eyes to why R0 isnt the be-all-end-all of covid contagiousness data - the "average contagiousness" or number of people infected by each infected person is only relevant if everyone has an equal chance at infecting others, where in reality MOST infections are spread by relatively few people.

Using this idea as a background, if the spread was always mostly being fed by a realtively small and irresponsible subgroup to begin with, then the "average vaccination" rates arent particularly enlightening bc it seems fair to assume it would include too many of the people who didnt contribute to the spread before and not enough of those who did.
posted by Exceptional_Hubris at 8:51 AM on April 8 [5 favorites]


Epidemiologist here. There are multiple factors that relate to your question, and steveminutillo has the main one. In a population that mixes with ease, the threshold for seeing population-level protective effects from the individual vaccination rate is almost always higher than people imagine. See also, we have flu vaccines that could quite literally nip annual surges of the illness in the bud (even when the vaccines aren't very effective), but in the US only about a quarter of the population routinely gets vaccinated. Here's hoping this knowledge permeates the popular consciousness and vaccination rates across the board go through the roof this year (hint hint).
posted by late afternoon dreaming hotel at 9:10 AM on April 8 [16 favorites]


If this were a computer virus I would say that only 30% of people using anti-malware, not opening links in emails without vetting, using strong passwords that are stored securely, only entered on secure sites, and not shared with others is not going to have a significant impact on computer fraud and corporate data breaches. And when I look at the consumer tech world around me that's what I see. Hopefully this is not off topic but rather a direct analogy to the sorry state of affairs we have ended up in.
posted by forthright at 9:49 AM on April 8


Population dynamicist here. There are a million factors that control what rate of vaccination is necessary to suppress an infectious disease. Features of the pathogen, features of the host, features of how the hosts move and behave, features of the vaccine, etc.
This interactive simulation shows you how things can run under a few different scenarios and vax levels, and what is needed for herd immunity.
posted by SaltySalticid at 9:52 AM on April 8 [4 favorites]


I don't think anyone's mentioned the lag time as well -- the journey from not-immune to immune of a vaccinated individual is a number of weeks long, right? It's not quite a binary yes/no. So we'd expect the immunity attributable to vaccines to train the number of vaccines themselves by some number of weeks.
posted by chesty_a_arthur at 9:53 AM on April 8 [2 favorites]


And in addition to the vaccine immunity lag time, there’s also the fact that COVID has a long incubation period. So anything that affects transmission rates won’t show up in case data for a couple of weeks.
posted by showbiz_liz at 10:12 AM on April 8 [1 favorite]


Another thing to consider is that all the states have had wildly different standards when it comes to who can and can't be vaccinated. For example: let's look at a hypothetical tri-state area (which I am basing on things I've heard in actual states, but not actual neighboring states).

* State "A" opens things up to people 65 and older on February 1st. They do not offer any other eligibility. However, they allow people who live in State "B" or "C" but work in State "A" to get a vaccine there.

* State "B", next door, opens things up to people 75 and older on February 1st - but they also include people with "medical co-morbidities". That list of co-morbidities includes diabetes, cancer, heart disease and hypertension. They do NOT allow people who just work in state "B" to get the vaccine, you have to be someone who "Lives" in State "B".

* State "C", the third state, also has a list of co-morbidities - but heart disease is NOT on that list. However, they are open to people 55 and older on February 1st. They also allow people who live in state "A" but work in state "C" to get a vaccine - but not people who live in state "B".

So if I lived in one of those states, it is kind of a crapshoot as to whether or not I would be able to get the vaccine: if I was 62, I could get the vaccine if I lived in state C, or if I lived in state A but worked in state C. Or if I lived in State B and had heart disease. If I was 58 and had heart disease, however, I could only get the vaccine if I either lived in state C or state B. If I lived in state A and had heart disease, I wouldn't be eligible yet.

And as if all that wasn't bad enough - now throw in that since this is a tri-state area, there's a tri-state transit system connecting these 3 states that all 3 of them use, and so that unvaccinated 58 year old with heart disease in state A might be on the same commuter train as a vaccinated 58 year old who lives in state C but works in State A, or a vaccinated 68 year old from state B who's come in to state A to visit their grandkids; or that unvaccinated 58 year old with heart disease might live in state A but they have to work in state B and so they're forced into even closer quarters with a greater number of unvaccinated people...

I understand that that's complicated; my ultimate point is that we do not have a consistent national rollout plan for the vaccine, and have instead gone with a piecemeal, state-by-state rollout where they each set their own guidelines for who is eligible and who isn't. Now, that would work if everyone spent 100% of their time in their own state. But that is not the case - we all cross state lines for any number of reasons, and in some cases we are compelled to, and that can put someone at a greater risk.
posted by EmpressCallipygos at 10:12 AM on April 8


A few other things I suspect are happening with Covid specifically.

1. Because we started vaccinating the most vulnerable or likely to be infected first, a substantial portion of people who have been vaccinated probably already had some immunity from having previously been infected (we still don't have great data on the rates of asymptomatic infection).

2. The B.1.1.7 strain is much more infectious and became the dominant strain during that time. There's evidence that suggests that it's more infectious to kids specifically and this coincided with an increase of returning to in-person classes.

3. As noted above, we have done a poor job of getting vaccines to at-risk minorities. Having a full computer and fast/reliable internet, lots of time to spend hunting down appointments, and the ability to take time off from work to drive to a rural area all corelate with having the privilege to effectively isolate yourself and lower your risk.

4. There's a huge portion of the population refusing to vaccinate or wear masks, which provides ample breeding ground for Covid.

5. States started relaxing restrictions too soon in the vaccination process, encouraging risky behavior.
posted by Candleman at 10:25 AM on April 8 [1 favorite]


The above answers are excellent. In addition to these real world nuisances, you have a misunderstanding of R0.

R0 is mean infectious period x infection producing contacts per unit time. A 30% vaccination rate has no effect on the mean infectious period so even before you add any complexities of real life, it is not just a 30% reduction in R0.

Let's say it is R0=1.1 (which is way lower than the estimates in the literature). Then that is a 10 day infectious period x some rate. That gives us a rate per day of .11. If the 30% vaccination rate in the population reduces the infection rate per a unit of time by 30%, then .11 becomes .077.

The new R0 is .077 * 10 = .77 which is below 1 but not .70. We might be tempted to get hand wavy and say "it's only .07 difference" but do not get hand wavy with exponents related to people's lives.

So even if we want a toy model, a 30% vaccination rate doesn't result in a 30% reduction in R0 because R0 is not just transmission rate.
posted by bdc34 at 11:18 AM on April 8 [1 favorite]


Young folks are getting it in higher numbers; the most common variants now are the more contagious ones.

The NY Times says states with highest case numbers also have higher percentages of the more contagious variants (which makes sense, right?). Another article says that the British variant is the most common one in the US now.

This article focuses on Oregon, but gives some insight:
New COVID-19 case counts have plummeted in Oregon since late last year, but the state is experiencing a change in who is testing positive. Since January, the share of new cases in Oregonians aged 10 to 19 has grown by roughly 50% while the proportion of those aged 20 to 50 has shrunk, according to an analysis by The Lund Report.

This shift appears to be part of a national trend. Nationwide weekly data collected by the American Academy of Pediatrics show a similar rise in the percentage of new cases in the young. Hospital admission data exhibit the same pattern: The fraction of patients admitted to a hospital for COVID who are under 19 has nearly doubled since January....

But immunizing those who are already hunkered down may have less impact on cutting virus counts overall than vaccinating those who are most at risk, like essential workers. Case counts have fallen farthest in those aged 20 to 50, which includes a large fraction of those vaccinated in Oregon first: medical workers and teachers.

Another factor to consider is the spread of variants -- from Britain, South Africa and Brazil -- and ones emerging in the United States.

posted by bluedaisy at 1:27 PM on April 8 [2 favorites]


The Zeynep Tufekci article linked by Exceptional_Hubris explains this at greater length, but: R0 is an average. The old joke about averages is that if you put one foot in a bucket of ice and scald the other, you'll be quite comfortable.

All else being equal, if you could confer effective immunity to a uniformly distributed 30% of a population, that would reduce R0 in that population by 30% (bdc34, that's exactly what happens in your toy model). That's not where the flaw is. The flaw is in the assumptions -- "all else being equal", "uniformly distributed" -- and above all in thinking of R0 as a single global number. There are going to be hot spots long after most of the country/world has cooled down.

(This is not to disparage the many complexities acknowledged in other comments, I just wanted to tackle the R0 thing head-on.)
posted by aws17576 at 3:04 PM on April 8 [2 favorites]


Adding to Candleman's list that B.1.1.7 is not even the only extra-contagious variant out there now, just (for now) the commonest in the US.
posted by humbug at 5:01 PM on April 8


R0 estimates in the absence of lockdowns have ranged from about 2 to about 6 for this virus. I don't know if there was a final agreed number - it might not even be a sensible question since it will always vary dependent on environment and exposures - but a 30% decrease off an R0 of 2.3 is still 1.6. So you don't need a lot of "pandemic fatigue" or optimism, to keep R0 above 1.... Just less above 1 than it would have been.
posted by Lady Li at 7:16 PM on April 8


Response by poster: Oops, I did make a mistake in my already naive math, I was thinking about the vaccination rate in terms of percentage points of R and that's definitely wrong. Thanks to everyone who pointed it out. To update it a bit, let's say we have 1/3 vaccinated, and an R of 1.2. Assuming uniform distribution, no variants, etc., then you would see R drop to 0.8 (2/3rds of 1.2). However, that assumption of uniform distribution is the real rub here. Out of many helpful answers here, Exceptional Hubris's link reminded me of the term that had slipped my mind: overdispersed. Basically, the property that most spread (something like 80%) is in super-spreader events. Ones where none of the layers of swiss cheese are present, so speak. So the average R is particularly unhelpful at anything except a population-level calculation of spread. And when you throw in saeculorum's suggestion that the likelihood that those who are most likely to be vaccinated are the most likely to already be taking precautions and the least likely to be spreading, it's easy to see why the overall case rate isn't going down. That's even before you start talking variants, re-opening, delays in incubation and immune response, etc.

FYI, the current median R in the U.S. is 1.00, and the 90% confidence interval is 0.77 – 1.20.
posted by wnissen at 10:09 AM on April 9


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