The Path to Herd Immunization

Assumptions about the current situation:

  • Around 2.8 percent of Americans are currently infected with covid.
  • The dominant strain of covid-19 has a basic reproduction rate (R0) of 2.4; i.e., left unchecked, each person infected with the virus will in turn infect an average of 2.4 other people.
  • Covid infection rates are currently at a steady state; i.e., each newly infected person is in turn infecting one other person. Steady-state contagion is attributable in part to preventive measures (masks, social distancing, etc.), in part to the reduction in the number of people who can contract the disease because they’ve already been infected.
  • About 18 percent of the US population has already been infected with covid, leaving 82 percent vulnerable to contagion.
  • Therefore, the current effective contagion rate of the virus (Rt) is 1.0/0.82 = 1.25. I.e., people infected with the virus infect on average 1.25 other people who have not previously been infected.

Assumptions about the first three months of 2021:

  • Current levels of prevention  (masks, social distancing, etc.) will persist; i.e., effective Rt will remain at 1.25.
  • People remain infected for around 2 weeks before becoming immune (or dying). So, over the next 3 months = 13 weeks, an additional 2.8 x (13/2) = another 18 percent of Americans will have become infected, bringing the cumulative total to around 36 percent.
  • Multiply 1.25 (Rt) by .64 (Americans still vulnerable to contagion) = 0.8. I.e., by the beginning of April 2021 the rate of new covid infections would be decreasing by 20% every two weeks.
  • At that rate, the pandemic would run its course in about a year; i.e., by April 2022.

Now factor in assumptions about the covid vaccine over the next three months:

  • The FDA-approved vaccines are 95% effective against the dominant strain of the virus.
  • By the end of March 2021, 40 percent of the US population will have been vaccinated.
  • Now, by early April, the percentage of Americans still vulnerable to infection would be around .6 (unvaccinated) x .7 (not yet infected) = 40 percent.
  • Multiply 1.25 x .4 = 50% reduction in new covid infections every two weeks beginning in April.
  • At that rate, the pandemic would have run its course in 5 months; i.e., by about September 2021.

Other variables not factored into these assumptions that would increase infection rates and delay the extinction of the pandemic:

  • New, more contagious strains of the virus, for which the vaccines might not be as effective, might spread rapidly.
  • The general public, becoming totally reliant on the vaccine, might abandon other preventive behaviors that suppress contagion.
  • Logistical and behavioral and psychosocial fuckups slowing down the initial vaccine rollout might persist, lowering the percentage of people getting the shots.



6 thoughts on “The Path to Herd Immunization

  1. I hope for the speediest remedy, of course, but it is amazing that it will have run its course regardless by April of 2022. Will the states will be able to complete the administration of the vaccine despite the evident early missteps? Fingers crossed…

    Liked by 1 person

  2. My covid vaccine timeline probably is overly optimistic. Biden’s vaccine plan calls for 100 million shots in the first 100 days. That’s only 50 million 2-shot immunizations — 15 percent of the US population — by the end of April. So maybe push everything out by two months.

    Part of the logjam is that the manufacturers aren’t just going to meet the US demand first; they’ve got contracts around the world. The flu vaccine already has several manufacturers, and they’ve got months to crank up the production between flu seasons, so they can supply more doses more quickly. There are 3 more covid vaccines in late-stage clinical trials, and if they’re like the others they’ll have already manufactured large quantities of them in anticipation of successful research outcomes. And preliminary findings suggest that the existing vaccines will be nearly as effective in immunizing against the new mutated forms of the virus.

    Of course optimism is a relative thing when talking about the US, or most of Europe and South America and even Canada for that matter. Even a vaccine that’s 90 percent effective provides less protection than living in a place like Australia where the baseline risk is minuscule even without a vaccine. Not to mention the 350,000 people who’ve already died in the US from coronavirus, with another 80,000 dying every month. On some disturbing level this has become the new normal here.

    Liked by 1 person

  3. Here’s the last two sentences from a WaPo editorial co-written by the dept. chair of UCSF Med School and the dean of Brown’s school of public health: “Giving 100 million people — particularly those at high risk — a single shot that is 80 to 90 percent effective will save far more lives than giving 50 million people two shots that are 95 percent effective. It’s what we should do.” Right on.

    Liked by 1 person

  4. Update on this post as of 30 January 2021:

    So far, per WaPo, 23 million vaccine shots have been administered in the US: 5 million people have had both shots, while another 13 million have had the first shot. Vaccines are being administered at the rate of 1.25 million per day. At that rate, 37 million shots will be administered per month. Starting in February, about 33 million more Americans per month will be fully vaccinated, or about 10% of the population per month.

    Let’s assume that the new mutants are more contagious, so that starting in February new infections will increase to 7% of the population per month.

    The easy math would say that immunity will increase by 17% of the population per month, or 51% over the next 3 months. Add that to the 21% who’ve already been infected and the 5% who’ve been vaccinated, and we’re at 76% immune by the end of April.

    But the vaccine isn’t 100% effective, and some proportion of those who get immunized will have previously been covid-infected. Let’s assume that the two-shot vaccine is 85% effective across all variants of the virus, but maybe 30% of those vaccinated over the next 3 months will have already been infected and so are 100% immune. Which also means that, of the 35% of the population who will have received the vaccine by the end of April, .35 x .30 = 10% will have already been infected. The combination of less-than-total effectiveness of the vaccine and vaccination of previously infected people reduces the total level of immunity by the end of April to about 70 percent.

    Which is pretty darned high. But if the new mutation is more contagious, the threshold for herd immunity tipping point goes up. Push it out one more month to the end of May. So even with the more contagious variant and the less-than-optimal speed of vaccination, we’re still pretty close to the original timeline of the virus having largely run its course by September.


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