26 United States The EconomistJuly 25th 2020
W
hy have covid-19 cases risen so fast?
The answer may seem blindingly ob-
vious. But it is not. And the implications of
the real answer are even more worrying
than those of the obvious one.
The manifest and palpable explanation
is that, when lockdowns were eased, peo-
ple started moving around more, and those
who were infected started passing the virus
on. This is consistent with the chronology.
Most states began to lift restrictions
around the end of April or the start of May.
Allowing a few weeks for the disease to de-
velop brings you to the start of June when
cases began their recent spike.
This is not wrong, but nor is it the whole
story, because the pattern of people’s activ-
ity does not match the pattern of infection.
As the chart shows, new infections fell
gradually and gently from 100 cases per
million people in mid-April to about 60 in
mid-June. America at this point seemed to
be following Europe and East Asia down
the other side of the mountain of infec-
tions. But in mid-June, something extraor-
dinary happened. Infections exploded, in-
creasing fourfold in the next four weeks.
Indices of day-to-day activity, however,
show a different pattern. Such data, which
are based on mobile-phone tracking, reveal
no real change as lockdowns were eased.
Unacast, an American-Norwegian firm
that provides information to retail busi-
nesses, uses anonymised phone data to
track how far people are travelling, how of-
ten they are making non-essential visits
(for example, to cinemas or restaurants)
and how often they are meeting others. All
three indices show a big fall in activity un-
til mid-April (ie, early in the pandemic),
then a wobbly, gradual rise from April to
now. As lockdowns ended, most people did
not stampede to bars or beaches. Safe-
Graph, another retail-information com-
pany, shows a similar pattern in visits to
restaurants, shops and hotels. Human-ac-
tivity levels have increased linearly and
gradually since April, whereas coronavirus
cases first fell, then rose exponentially.
Does that mean the easing of lockdowns is
not to blame, because it has not made a
clear difference to people’s behaviour or to
the spread of the virus? In a word: no.
The explanation for the pattern of
American infections lies in something of
central importance to the spread of a virus:
geometric progression, such as 1, 2, 4, 8, 16.
If one person infects two, two infect fourandsoon.Unless the rate of infection is
driven down by reducing contacts, any
geometric increase quickly balloons: 256,
512, 1,024. This is the lesson of the inventor
of chess, who in legend asked, as a reward,
for one grain of rice on the first square and
twice as many on each successive square.
There was not enough rice in India to pay
his reward. That is one explanation for
America’s explosively rising caseload.
With almost 4m infections, the country is
on square 23.
Another explanation is that the starting
point matters. If you begin a geometric pro-
gression at one, the tenth in the sequence is- If you begin at three, the tenth iteration
is 1,536. American states began easing lock-
downs, as it were, at three: their caseloads
were three or more times higher than in
Europe, in part, argues Jarbas Barbosa of
the Pan-American Health Organisation, be-
cause most states never had full lock-
downs. Texas had 1,270 new cases on the
day its governor said restaurants could re-
open: 44 per million. In Georgia, the rate
was 95 per million. Disney World reopened
the day before Florida announced a record
15,000 new cases in a day. Just as incredibly,
in two-thirds of states, infections were ris-
ing when governors started to ease lock-
downs. By contrast, France, Spain and Italy
had 13-17 new cases per million when they
began to re-open their economies and
numbers were falling fast.
Rajiv Rimal of Johns Hopkins Universi-
ty has modelled the effect on infections of
different levels of activity. On April 12th, he
reckons, 95% of the population was staying
at home (leaving the house only for essen-
tial visits), with 5% ignoring lockdown
rules. Based on those assumptions, his
model predicts that America would have
had 559,400 cases on that day—an accurate
assessment (it actually had 554,849). On
July 14th, Mr Rimal assumed that 80% of
the population was staying at home, ie,
only a gradual change. On this basis, his
model predicts the country would have
3.6m cases, again not far off the actual
number and confirming the impact of
modest rises in activity. If people really al-
ter their behaviour, the number would rise
even further: to 5.6m cases if the stay-at-
home share drops to 60% and to 9.5m if it
falls to 20%. In that worst case, America’s
death toll could top 400,000. Such is the
dark logic of geometric growth.
The implication of these figures is that,
when the virus is widespread, even small
amounts of activity can make infections
soar. You do not need vast, mask-less
crowds, though America had those, too. So
the public-health task is clear: to drive the
level of infection down to perhaps a tenth
of what it is now (closer to European or
Asian levels). That seems to require full
lockdowns. At the moment, few politicians
seem prepared for such a thing. True, nine
states have reversed some restrictions and
13 have paused their reopenings. At his first
televised news conference about the virus
since late April, President Donald Trump
urged people to “get a mask”. But no gover-
nor has yet been willing to tell everyone to
stay home. Some reopenings continue and
Georgia’s governor sued the mayor of At-
lanta when she ordered people to wear
masks. “We’re having a dozen New Yorks
all over the country,” says Peter Hotez, of
the Texas Children’s Hospital in Houston.
“It’s predominantly in low-income metro
areas. Hispanic communities are being
devastated. And there’s no leadership deal-
ing with it.” 7It’s not just beaches and bars. Even modest changes in behaviour can cause huge
rises in coronavirus infectionsEasing lockdowns and covid-19The geometry of the pandemic
Here’s howCollateral damage
Covid-19, daily new confirmed cases per 1m people
2020, seven-day moving averageSources:EuropeanCentreforDiseasePrevention
andControl;JohnsHopkinsUniversityCSSE200150100500
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