Are We Approaching Herd Immunity?

In a Wall Street Journal opinion piece from 17 February, Johns Hopkins surgery professor Marty Makary claims that the US will reach covid-19 herd immunity by the beginning of April — that’s a little more than a month from now.

According to Makary, by the end of March, 250 million vaccines will have  been administered to Americans. That seems wildly optimistic: so far 63 million shots have been administered, and at the current rate that number would double to around 125 million — half of Makary’s projection.

Makary also asserts that a far greater proportion of the population has been infected by the covid virus than is indicated either by case counts or by antibody testing:

“Testing has been capturing only from 10% to 25% of infections, depending on when during the pandemic someone got the virus. Applying a time-weighted case capture average of 1 in 6.5 to the cumulative 28 million confirmed cases would mean about 55% of Americans have natural immunity.”

That assertion is likely based on a CDC report from June which I quoted in a post at the time:

“Our best estimate right now is that for every case that’s reported, there actually are 10 other infections,” CDC Director Dr. Robert Redfield said on a call with reporters Thursday.”

But that was before testing ramped up in the US. From the beginning of the outbreak through June, the US administered around 250K diagnostic tests per day. Since then, the testing rate has averaged around 1.25 million per day — 5 times the earlier testing  rate, capturing a far higher proportion of infections than previously.

Also in June, the CDC reported preliminary findings from several seroprevalence surveys conducted in the US, suggesting a higher rate of infections, and a lower fatality rate, than prior estimates. Makary’s covid fatality rate is derived from this earlier CDC study:

“The Covid-19 infection fatality rate is about 0.23%. These numbers indicate that roughly two-thirds of the U.S. population has had the infection.”

However, in early July, after all the serology data had been analyzed, the CDC revised their estimates, doubling the fatality rate while halving the prevalence rate. By late July the CDC had increased its estimated fatality rate further, to around 0.6 percent, which for 500K deaths to date would put the US population prevalence at around 25 percent. Other epidemiologists converge on or near this updated CDC covid fatality rate estimate for the US; so do I.

Makary observes that antibody tests “almost certainly underestimate natural immunity.” That’s almost certainly an overstatement. An August BMJ editorial speculated that finger-stick antibody tests, which identify IgC antibodies, might undercount IgA antibodies. However, a Mass General study found that covid IgA antibodies spike soon after infection and then decline even more rapidly than IgC antibodies. A relatively straightforward study could evaluate the sensitivity of antibody tests over time: identify a group of people who have tested positive on a covid diagnostic test, then administer antibody serology tests to them over the next several months to determine whether and when their antibodies are no longer detected. A number of US universities regularly test their students and staff for covid infection regardless of symptomatology: it would be easy to sample a subset of these test-positives and follow them over time.

Makary stakes his strongest claim in his very first sentence:

“Amid the dire Covid warnings, one crucial fact has been largely ignored: Cases are down 77% over the past six weeks.”

He’s right: covid infections have dropped precipitously so far this year. Makary insists that the rapid decline “can be explained only by natural immunity.” Granted, the reduced infection rate is puzzling. There’s no evidence to suggest that Americans have suddenly gotten religion about social distancing and masking up and self-quarantining. If, as Makary contends, two-thirds of Americans have already been infected by the virus, the rate of viral contagion would be dropping for lack of new bodies to infect.

However, rates have also been dropping just as rapidly in other countries with lower covid prevalence rates than the US. Cumulatively, about 1,500 per million population have died of covid in the US; using Makary’s 0.23% fatality rate that comes out to 65% of the American population, as he says in the article. In Canada about 570 per million have died of covid. Per Makary that would translate to around 25 percent of the Canadian population having been infected — far from herd immunity — and yet Canada’s infections have been dropping as fast as the US’s. Ireland: 830 deaths per million, 36% infected, infections dropping even faster than in the US and Canada. There are others.

To be sure, some countries in the world are approaching covid herd immunity. Using the more widely accepted 0.6% fatality rate and adjusting downward to accommodate the relatively young median age of the population compared to the US, around 64% of Bolivians have been covid-infected. If Makary’s 0.23% fatality rate were used instead, then around 166 percent of the Bolivian population would have already had covid. Peru, Colombia, Mexico, Ecuador, Panama, Guatemala, South Africa, Iraq — all would have covid prevalences over 100 percent by age-adjusting Makary’s fatality rate and prevalence estimates.

More compelling still are infection rates of subpopulations within the United States. In my most recent post I estimated that 67 percent of Hispanic Americans have already been infected by the covid virus. In calculating this estimate I used published death counts and a 0.65% fatality rate, age-adjusted for the Hispanic American subpopulation. Sixty-seven percent infected: that’s the number that Makary attributes to the US population as a whole, creating herd immunity and triggering the rapid nationwide decrease in case counts. But what if it’s only the Hispanic Americans who have passed the herd immunity threshold: could a rapid decrease in new infections among that subpopulation of Americans account for the overall decrease in America as a whole? Yes. According to my calculations, Hispanics have accounted for 60 percent of all the covid infections in the US. In contrast, I calculate that only 8 percent of white Americans have been infected. Social distancing isn’t just behavioral; it’s also structural, with white Americans buffered from their Hispanic compatriots by fairly rigid racial, cultural, residential, and economic boundaries.

As Derek Thompson observes in a 17 February Atlantic article:

“America’s seroprevalence—that is, the number of people with coronavirus antibodies from a previous infection—is not randomly distributed across the country. Instead, immunity is probably concentrated among people who had little opportunity to avoid the disease, such as homeless people, frontline and essential workers, and people living in crowded multigenerational homes… What I’m describing here is not herd immunity… But it is partial immunity among the very populations that have been most likely to contract the disease, perhaps narrowing the path forward for the original SARS-CoV-2.”

Perhaps similar class hierarchies are at work in Canada and Ireland and other countries with declining infection rates, “narrowing the path forward” through widespread contagion among the most vulnerable sub-herds.

All Else Is Not Equal: Racial Disparities in US Covid Casualties

How many people in the US have contracted covid since the beginning of the outbreak? Case counts of diagnostic test-positives underestimate the number of infections because a sizable percentage of people who’ve been infected never get tested. Death counts are a more accurate lagging indicator of infections, because deaths are relatively more accurately recorded and because a relatively stable percentage of people who get infected eventually die from the disease. According to my quick-and-dirty algorithm, the total number of covid infections equals the total number of covid deaths divided by .0065. As of 18 February 2021 there have been 505K covid deaths in the US, which translate into 77.7 million covid infections. The population of the US is 329 million, so around 24 percent of Americans have been infected with covid.

All else equal, older people who get infected are more likely to die from covid than are infected younger people; consequently, the divisor in the deaths-to-infections algorithm is age-adjusted. The median age of the US population is 38 years. For populations with a higher median age than the US, the .0065 divisor is increased by 1.1 to the Dth power, where D = the difference in median age from 38. For populations with a lower median age than the US, the divisor is decreased by 1.1 to the Dth power.

According to the CDC, Hispanic Americans are 2.3 times as likely to die of covid as are white Americans, while blacks are 1.9 times as likely as whites. All else equal, it would be expected that this racial discrepancy in fatalities could be explained by median age differences. Adjusting upward from the .0065 covid fatality rate, the median age for Hispanics would project to be about 8 years older than whites (1.18 = 2.1), whereas blacks would be 7 years older than whites (1.17 = 1.9). In fact, however, the median age for white Americans is 44 years, whereas for Hispanics it’s 30 years — 14 years younger than whites — and for blacks it’s 35 years — 9 years younger than whites. All else equal then, the algorithm would project a Hispanic covid fatality rate of 1.1-14 = 3.8 times less than whites; for blacks, a covid fatality rate of 1.1-9 = 2.4 times less than whites. So, taking into account the relatively young age of these minority groups, their high covid fatality rates for US minorities are even more glaring than the raw numbers indicate.

To calculate the relative risk of covid infections for Hispanic and black Americans relative to white Americans, multiply their observed relative risk of their having died of covid by their age-adjusted relative expectation of covid mortality based on the algorithm:

  • Hispanic = 2.3 x 3.8 = 8.7 times as likely as whites to have been covid-infected
  • Black = 1.9 x 2.4 = 4.6 times as likely as whites to have been covid-infected

The US population is roughly 60 percent white, 19 percent Hispanic, 12 percent black, 9 percent mixed or other. For simplicity’s sake, I’ll eliminate the mixed/other category, rounding the numbers to 66% white, 21% Hispanic, and 13% black. Of the total number of Americans who’ve been infected by covid, the racial proportions are estimated as:

White (.66 x 1) + Hispanic (.21 x 8.7) + Black (.13 x 4.6) = 0.66 + 1.83 + 0.60 = 3.09

  • White = .66/3.09 = 21% of US covid infections.
  • Hispanic = 1.83/3.09 = 59% of US covid infections.
  • Black = .60/3.09 = 19% of US covid infections.

If these estimates are roughly accurate, then of every five Americans who have been covid-infected to date, one is white, one is black, and three are Hispanic.

Overall, 24 percent of Americans have been infected by the covid-19 virus since the beginning of the outbreak. What proportion of the members of each of the big three racial groups have been infected?

  • White = 21% of the 24% infected, divided by 66% of the population = 8% have been infected.
  • Hispanic = 59% of the 24% infected, divided by 21% of the population = 67% have been infected.
  • Black = 19% of the 24% infected, divided by 12% of the population = 38% have been infected.

Again if the estimates are roughly accurate, then Hispanics are approaching the threshold for herd immunity in the US, even before widespread vaccination.

The estimated racial disparities in covid infection rates are likely overstated. All else equal, a 38-year-old infected with the coronavirus has a 0.65% chance of dying from the infection, irrespective of race. But all else isn’t equal. American Hispanics and blacks in America tend to have more comorbid conditions for their age than do their white counterparts, so a relatively higher proportion of their infections prove fatal. Which is a more dire indicator of racial disparity: a higher infection rate, or a higher fatality rate? In the US, Hispanics and blacks suffer massively from both.