Serology by country
Antibody surveys measure the infected share directly. Where contacts were cut, first waves turned over with 1-5% infected; in Manaus, with little control, the immunity factor was 2.5 and infection went on to 66-76%.
The method
Growth comes from the contiguous rise of daily hospital admissions, intensive-care admissions or deaths, converted to $R$ as on US county waves.
Antibodies found on date $t$ reflect infections up to about $t - 14$ days, which correspond to deaths up to about $t + 7$ days. The infected share at the turnover is the survey prevalence scaled back to the death peak:
$$a_{\text{turn}} = \text{prevalence}(t)\;\frac{D(\text{death peak})}{D(t + 7\ \text{days})},$$where $D$ is cumulative deaths.
Summary
| place | survey | control | $R$ from growth | infected at the turnover | $\lambda$ |
|---|---|---|---|---|---|
| England, 9 regions | REACT-2 round 1 | lockdown 23 March | 2.1-3.5 | 0.9-5.0% | 17-94 |
| Geneva | SEROCoV-POP | closures 16 March | 3.3 | 5.1% | 23 |
| Stockholm | FHM outpatient; Castro Dopico et al. | voluntary | 2.8 | 2.3-3.1% | 33-44 |
| Skåne, Västra Götaland | FHM outpatient | voluntary | 1.7-1.8 | 1.2-2.9% | 20-45 |
| Spain, 52 provinces, spring | ENE-COVID round 3 | lockdown 14 March | 1.9-4.3 | 0.3-4.6% | about 60 |
| Spain, 24 provinces, autumn | ENE-COVID round 4 | curfew 25 October | 1.1-1.5 | 2.6% of susceptibles | about 7 |
| Manaus | Buss et al., blood donors | little effective control | 1.6 | about 17% | 2.5 |
Spain
The ENE-COVID survey (Pollán et al. 2020) tested a national sample in every province, in rounds from April to November 2020.
In spring, hospital admissions peaked between 23 and 31 March in almost every province, 9-17 days after the national lockdown of 14 March, whatever the province's growth rate or immunity. The lockdown set the turnover. Growth read from admissions and from deaths is uncorrelated across provinces (0.04), so the provinces cannot measure how depletion varies with growth.
In autumn, round 4 measured infection among people still susceptible after the first wave. The waves turned over having infected a median 2.6% of them, against a textbook 17%. The national curfew of 25 October 2020 overlaps the peaks.
Sweden
Sweden had no lockdown, but it did have a ban on gatherings of more than 50 from 29 March 2020, advice for people over 70 to limit contacts from 16 March, distance teaching in upper-secondary schools and universities, and a large voluntary drop in contacts.
Intensive-care admissions in Stockholm peaked on 4 April. Serology from the Public Health Agency's outpatient survey and from blood donors and pregnant women (Castro Dopico et al. 2021) puts the infected share at that turnover near 2-3%.
The paradox was first noticed in Sweden. Its first wave turned over too early for immunity, even with heterogeneity, to explain; the voluntary cut in contacts did.
England and Geneva
REACT-2 (Ward et al. 2021) tested about 100,000 adults by region in June and July 2020. Deaths by date of death peaked between 6 and 18 April, two to four weeks after the lockdown of 23 March. London turned over with 5% infected and $\lambda = 17$.
SEROCoV-POP (Stringhini et al. 2020) measured 10.8% in Geneva in early May. Deaths there peaked on 7 April, with 5.1% infected at the turnover.
Manaus
Blood-donor serology (Buss et al. 2021), corrected for test performance and waning antibodies, rose from 5% in mid-April 2020 to 46% in mid-May and 66% by July, reaching 76% by October.
Excess deaths grew at a rate that reads as $R = 1.6$, with a textbook threshold of 38%. The first wave turned in late April with about 17% infected, an immunity factor of 2.5. That is the value contact surveys predict (age and activity).
Infection then continued to 66-76%, close to the homogeneous final size of 65% at $R = 1.6$. Fixed heterogeneity with $\lambda = 2.5$ would have stopped it near 35%. So the early turnover was temporary, as activity that changes over time predicts.
Blood donors are not the whole population, the surveys are monthly, and the 76% estimate has been disputed. The infected share at the turnover is interpolated between the April and May surveys.
Code: analysis scripts 10, 11, 13 and 14. Sources for every file, table and page are listed in fetch/.