Where and when does herd immunity kick in?

Here is the abstract of a new paper by Axel S Lexmond, Carlijn JA Nouwen, and John Paul Callan. So herd immunity yes, but at some point after fifty percent:

We have studied the evolution of COVID-19 in 12 low and middle income countries in which reported cases have peaked and declined rapidly in the past 2-3 months. In most of these countries the declines happened while control measures were consistent or even relaxing, and without signs of significant increases in cases that might indicate second waves. For the 12 countries we studied, the hypothesis that these countries have reached herd immunity warrants serious consideration. The Reed-Frost model, perhaps the simplest description for the evolution of cases in an epidemic, with only a few constant parameters, fits the observed case data remarkably well, and yields parameter values that are reasonable. The best-fitting curves suggest that the effective basic reproduction number in these countries ranged between 1.5 and 2.0, indicating that the curve was flattened in some countries but not suppressed by pushing the reproduction number below 1. The results suggest that between 51 and 80% of the population in these countries have been infected, and that between 0.05% and 2.50% of cases have been detected; values which are consistent with findings from serological and T-cell immunity studies. The infection rates, combined with data and estimates for deaths from COVID-19, allow us to estimate overall infection fatality rates for three of the countries. The values are lower than expected from reported infection fatality rates by age, based on data from several high-income countries, and the country population by age. COVID-19 may have a lower mortality risk in these three countries (to differing degrees in each country) than in high-income countries, due to differences in immune response, prior exposure to coronaviruses, disease characteristics or other factors. We find that the herd immunity hypothesis would not have fit the evolution of reported cases in several European countries, even just after the initial peaks; and subsequent resurgences of cases obviously prove that those countries have infection rates well below herd immunity levels. Our hypothesis that the 12 countries we studied have reached herd immunity should now be tested further, through serological and T cell immunity studies.

They offer an implied exposure estimate of 72% for Afghanistan, 67% for Ethiopia, 74% for Kenya, and 80% for Madagascar.  Pakistan clocks in at 72%, South Africa at 71%.  Notice those are not case counts, rather it is working backwards, using a model, to infer exposure rates from the data we do have, assuming that not all cases are being measured.

Here is mostly good NYT coverage on herd immunity theories, though in my view unfair on T-Cell immunity issues — they confuse uncertainty with “there is no reason to believe anything here.”  Here is a new and good NYT article on the Swedish approach.  The different pieces still do not all fit together.

Via Alan Goldhammer.

Addendum: From Catinthehat in the comments:

It’s a simple homogeneous model Ni(t+1)= Ni(t) * Ro * Si(t) / Ntot -> Infected at time t+1 = Infected at time t * Ro * the proportion ( of the population) susceptible at time t. where t is discretized.
They fit the step t to an infection duration , then they fit Ro, to reproduce the shape of the curve for each country and at each step they multiply the infected by a parameter p (the undetected case ratio) to fit to the total population. This acts as an accelerant to the epidemic . Each country has its own p.
The main issue is that you can look at any epidemic curve and fit it that way and you will rather automatically reproduce this high immunity threshold which comes from your homogenous model.

In Europe you can’t assume the undetected ratio is so high ( 1000x to 2000 x) so you must conclude social distancing stopped the epidemic, because your strategy would not fit experimental data.

In the countries fitted , the paper must conclude the epidemic raged fairly undetected, fairly quickly and infected most of the population.