Acquired Herd Immunity Via Vaccination

Let’s suppose that further clinical trials validate the preliminary numbers, and the new covid vaccine turns out to be 90 percent effective. I.e., the virus will infect only 10 percent of those who would have been infected had they not been vaccinated.

That’s great for those who get the shot, which would almost surely include me. What would be the vaccine’s impact on the pandemic if not everyone gets vaccinated?

Right now around half a percent of the US population is currently covid-infected and contagious. How long would it take for the virus, left unchecked, to spread through the entire population? Covid’s estimated reproduction rate, or R0, is around 2.5; i.e., if the virus is left unchecked by preventive measures, then on average every 4 people who’ve been infected with the virus will infect 4 x 2.5 = 10 other people before they’re no longer contagious. Those 10 newly infected people will in turn infect 25 more people, and so on — a geometrically increasing rate of contagion. People who’ve been infected remain contagious for around 10 days, so every 10 days the percentage of the population infected would increase to 2.5 times its prior rate. How many ten-day infection cycles would it take for the virus to infect everyone in the population?

0.5% x 2.56 = 122%

After 6 ten-day cycles — two months — of unabated contagion, everyone in the US would have been infected. Herd immunity would be “achieved” by the end of January 2021 via uncontrolled spread of the disease.

The virus isn’t totally out of control; various preventive measures — social distancing, masking up, etc. — are slowing the spread. Lately there’s been a spike in cases and a slower rise in deaths. Rt — the effective contagion rate — is now around 1.5 in the US. At this rate, all Americans will have been covid-infected after 10 10-week cycles, or 100 days. Herd immunity by mid-April 2021 — right around the time the vaccine would become widely available. Presumably behavioral restraints will tighten down and the rate of contagion will restabilize before that happens.

An effective vaccine can eventually lead to acquired herd immunity if the Rt drops below 1. Suppose a 90%-effective vaccination is approved and made widely available, while the Rt stays at its current level of 1.5. For those who take the vaccine, the Rt drops by 90%, to 0.15; for those who don’t take the vaccine, the Rt remains at 1.5. What percentage of the population would need to be vaccinated in order to bring the Rt below 1?

((1.5 x .1) x V) + (1.5 x (1 – V) < 1   –>   V > 0.33

I.e., at least a third of the population would need to be vaccinated in order to bring the effective reproduction rate below 1, eventually extinguishing community spread of the virus through acquired herd immunity. The higher the vaccination rate rises above 33 percent, the faster herd immunity can be achieved and the pandemic can be quashed.

What if, once the vaccine becomes available, people stop social distancing and wearing masks and so on? Then the Rt would return to the R0, or 2.5. Assuming 90% vaccine effectiveness and no behavioral constraints on contagion, how much of the population must be vaccinated in order to bring Rt below 1?

((2.5 x .1) x V) + (2.5 x (1 – V) < 1   –>   V > 0.67

I.e., at least two-thirds of the population would need to be vaccinated in order to bring the effective reproduction rate below 1, eventually extinguishing community viral spread through acquired herd immunity.

Bringing the Rt below 1 will be important not only for those who don’t get vaccinated. Antibodies degrade pretty rapidly over time, and so will the effectiveness of any individual’s acquired immunity via vaccination. If the virus continues to percolate through the population, people will need to be re-immunized periodically, perhaps as often as every 4 months, forever. If enough people get the shot, then the intervals between shots would be extended. Maybe, after a few rounds of widespread vaccination over the course of a couple of years, the virus, which seems not to mutate very rapidly, will effectively be extinguished from the population.

6 thoughts on “Acquired Herd Immunity Via Vaccination

  1. Today, 11/16, Moderna announced preliminary results showing 95% effectiveness of their vaccine. And final results aren’t far off:

    Moderna has committed to completing its trial before applying for emergency-use authorization — which means waiting until there are 151 cases of covid-19 in the study. A previous projection showed that the trial might end sometime early next year, but it is instead expected to reach its endpoint in seven to 10 days, Bancel said, because of surging coronavirus cases in the United States. The explosion of virus cases translates into an expedited ability to ascertain whether a vaccine works.

    The silver lining in the spike.


  2. A new study shows that covid immunity lasts for a long time, quickly mounting an effective response to new infection. I’d wondered why reinfection seemed not to be more common among those infected during the first wave in March and April. Flu vaccines wane in effectiveness after a few months, and people can catch a cold virus over and over in short order. It seems increasingly likely that these reinfections are due in large part to viral mutation. So far covid hasn’t mutated much, so the immune system’s “memory” of the virus remains relevant for a longer time.


  3. I’ve known for a while about all this meticulousness about Covid you’re doing. It’s very impressive, although I cannot work up any interest in Covid as such.

    I also noticed one cannot find dates on anything here (you may recall I’m a ‘date freak’ and a ‘place freak’, but I went through most of the posts under ‘Fan Fiction’. You have gone through all these phases since you started Ficticities, but you don’t seem to let it get you destabilized: It’s more normally balanced, wasn’t it one of the Obamas that said ‘never too high, never too low’. Of course, that’s the secret to some things, and definitely is the way not to go crazy in politics. It’s not the secret to other things. I can boast of my extremismi that takes various forms, simply because that’s the fact. It’s not even good (except to me), and it’s definitely considered bad by many if I disclose too much of it (which I do, most would say.)

    I think the one I started with was the one in which you would not (till the end, where you say it’s ‘maybe what you really do want’) want to be ‘inside these Ballardian writers’ world’, something like that anyway. I didn’t come here looking for Ballard and never think of him. All those British-left bloggers like Dominic, Fisher, Mackay, the rest, always took Ballard very seriously.

    I came here for much more prosaic reasons, but somewhat related. I’ve become addicted to Ian McEwan, having read his Enduring Love, to which I was tipped off by my ‘Rachilde’ troll who once signed in as ‘Clerambault’. He has a form of it, in fact, and although I knew basically the plot of the book, it wasn’t till I finished that I knew ‘Rachilde’ had a form of Clerembault’s Syndrome, and summarily fully finally dismissed him. His lies are quite beyond reproach in their viciousness. He actually thought, like the Clerembault sufferer in the McEwan book, that I ‘loved him’, and that he ‘felt it too’, almost exactly like Jad Parry and his victim, Joe Rose. In both cases, they were deeply involved with God, but I don’t think Rachilde has actually read the McEwan book. Or maybe he knew he was beaten, and that I was tired of plagiarized passages (DOZENS of them before I even discovered and told him I had discovered, DOZENS MORE.) Furthermore, he was using texts of interviews in LRB with someone else who was talking to someone else about her interview with Sontag. After I told him about reading Edmund White’s Caricole, whom he also claimed to know, he told me he was ‘genial’, among other things, and that all of his novels were ‘garbage’. (Caricole happened to be brilliant, but did not make me want to read more White, whereas Enduring Love makes me want to read at least two more (I’m on Saturday as of tonight), and definitely Atonement and then watch the movie, for which there was a lot of talk on the blogs in the late 00s. I think everybody knows him, and how I missed finding him I have no idea. He’s so different from writers like DeLillo, McEwan is actually *real fiction* that also has that page-turner technique. I was up till 6 a.m. finishing Enduring Love, simply couldn’t stop. Then read Amsterdam, for which he got the Man Booker. I want to read DeLillo’s recent one, but he’s got other virtues. Didion wrote only one page-turner, and I don’t think she even meant it to be (would look down on it.) But I think McEwan is a much better fiction writer than she is, and maybe even better than DeLillo, but that could just be that I’m infatuated.

    Those same die-hard Ballardians are also big Lovecraft readers, as Nick and Robin, and Nick is writing short pieces on Substack right now–they’re good, but I was more interested that he had the character say to himself ‘I am dead’ the same day I read the composer Linley to say exactly that (and the other main character–this is still Amsterdam also may have said those exact words, or close enough in that he felt himself ‘not to exist’ when he was alone). I have no truck with ‘synchronicity’, what difference does coincidence make, other than a little mild, not very substantial charm?

    But it was your post on Ballard that made me realize how little I think of his work. I read a couple of the later ones, Cocaine Nights and Super-Cannes, and, looking back, I noticed that some of it seemed like indigestible pulp even then, and definitely thought that about the excerpts you put from High Rise. He seemed to sometimes write what I might call “unreal fiction the pretends to be about real life as we know it”, You get whiffs of that in McEwan and Houellebecq, but Super-Canned was absurd–these business parks with all these professionals ‘doing what they love’, then slipping into pornographic fantasy. That’s such a common thing to do for the last 30 or 40 years.

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  4. Back when Ktismatics was active I wrote a couple of short posts about Atonement, one comparing it to the film treatment, the other linking it thematically to Henry James’s The Golden Bowl. I can’t remember whether I read McEwan’s first novel The Cement Garden before or after Atonement, but it too is excellent. At some point I’ll read Amsterdam and Enduring Love. The Durham library is closed, so I’d have to reserve the book and schedule a pickup time. Maybe I’ll give it a go, since I am looking for something else to read, being just about finished with Ford Madox Ford’s multi-volume Parade’s End.

    I’d forgotten that the posts here don’t have date stamps. When I originally set up Ficticities I wanted it to function more as a website than as a blog, so I didn’t want dates on the entries. The corona sequence though is intrinsically temporal, following the progression of the pandemic and of my understanding of it. After a quick look at the setup I’m not sure how to add the dates to the posts, but I’ll get back to it later.

    I agree about Ballard of course. The Atrocity Exhibition was a wild ride, but not something I’d ever return to. Super-Cannes was an atrocity not worth exhibiting. Arguably though we are living through a Ballardian era of dangerous surreal absurdity.


  5. The libraries being closed is a bitch. I’ve been finding this for 99 cents plus shipping, total just over $5 on eBay.. Hadn’t been interested in fiction for a long time. Weird thing is that these cheap books turn out to be unused hardcover editions that I can’t find any signs of wear. These wouldn’t come for 2 weeks or more, so I went to the new and used giant Strand Bookstore, and stood in my first Covid line. This was not too bad, not too cold. Hard for me to ujnderstand how meagre ‘coolness pickings’ are wnen young people think it’s worth it to stand in line for Trader Joe’s. Not that much cheaper and definitely not better than soime others. But they did it here with the Magnolia Bakery in Sex and the City and Tom’s in Seinfeld I never could see what people saw in these shows.

    I will read your ktismatics posts on Atonement after I’ve read and seen it. I don’t think NYPL offers this scheduling and picking up during Covid–there are 2 branches open way up in Harlem, and I haven’t taken public transportation in this. Your continued posts on the pandemic are very admirable, I don’t have those scientific and mathematical abilities developed (although I could do it as far as I had time to do when young–could never concentrated on now) and just read the headlines about what’s latest that you should do. At least you can have Thanksgiving at home, though, I’m going to make stuff anyway, and also go to a nice resto if they have it fixed with temporary plastic walls and heaters, unless they close these down again. Closed the schools here yesterday after 8 weeks.

    Might be Ballardian what we’re living through. Some of those business park atmospheres had elements of things like Davos in them. ‘Super-Cannes’ is not even mentioned till the last couple of chapters, otherwise the park has been called Eden-Olympia throughout–probably a commercial matter. It’s true that once Trump decided on these weeks of antics, it was clear that this constant hum of catastrophe of whatever kind would always be there–without giving us even a short break. it’s like what he’s doing is not different from the old stasis, it’s become part of it, even though the diehard supporters think he offers the only redemption, and think the early-morning calling of Wisconsin and Michigan proves beyond a shadow of a doubt that some ‘powers-that-be’ decided to ‘fix things’ that were looking too much like 2016. I could feel when there was the real slump, and thought Trump had won it, but they have no foundation to base this on, and Trump himself knows that didn’t happen. He just wants now to continue his ‘showman number’, and that proves that this numbness we’ve grown accustomed has never stopped–the violence and psychopathy in Ballard do necessarily grow out of the enforced boredom (or it feels enforced.) Ballard and McEwan (at least what I’ve read) do focus on the top professional classes, but McEwan’s characters seem human, if troubled, and like some I’ve known. Ballard’s seem like cartoon people to a great degree. Good ir you’re mostly a sci-fi reader. I guess Ballard is high sci-fi. I think McEwan had an early sci-fi or semi-sci-fi period–probably rare to find a writer to be able to make that transition. Terrible things happen, but it isn’t like Lovecraft, which I never intend to read. I’m allergic to sci-fi, I think, and Neil Stephenson’s The Diamond Age that Nick recommended and thought so great just seemed endlessly boring, full of all-new (then) techno-trinkets..

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  6. I’m rethinking the Ballardianism of our current events. You’re right that Ballard’s apocalyptics focus on the depravity of the top professional classes, which certainly doesn’t characterize Trump’s rubes. Maybe the more literate among them view the epidemiologists and climate scientists and election technologists and deep-state operatives and woke activists as Ballardians, grinding Western civilization to a halt with fake news and fraud while satisfying their perverse sadistic urges in secret pedophilia rings and dalliances with foreign powers bent on our destruction. This is starting to sound more like Houellebecq…

    I too tried one of Stephenson’s gigantic novels. It read like a kind of operating manual — I abandoned it after a hundred pages or so.

    I don’t recall if I mentioned it before, but the big high-tech R&D corridor in the south of France is called Super-Antibes. Antibes is the town between Nice and Cannes along the Côte d’Azur.


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