Quantitative analyses on the global coronavirus pandemic

Month: May 2020

Reopening Florida and Risk of Reinfection

Florida has reopened for business for four weeks now and its experience is similar to that encountered by other states and countries that are trying to reopen quickly after COVID-19 lockdowns.  Reopening the state for business is necessary and should be possible if enough testing and contact tracing resources are made available.  However, testing capacity has always been surprisingly problematic for the US since January 11th when the genetic code for the novel coronavirus was first published and major countries such as South Korea and Germany were able to produce valid tests in quantity.  To date, Florida and the US as a whole still lags behind South Korea, Germany, Taiwan, Australia, and other best-in-class countries in terms of testing completeness and thoroughness.

The figure below shows that testing (brown square against left axis) in Florida has expanded in two months from 6,000 per day in late March to near 24,000 per day now.  The percentage of test results returning positive (blue diamond against right axis) has dropped from near 12% to near 3% now.  All this is very encouraging although the unevenness of the recent data is worrisome especially in light of the recent complaints that (1) the data scientist compiling these data had been summarily dismissed, (2) thousands of tests have been invalidated because of poor handling, and (3) the count of virus tests and serological tests have been mixed inappropriately.  Moreover, the improvement in testing completeness, after briefly touching 1% has now settled around 3.5% — suggesting that the overall Florida population may still be highly infected.   

Another way to check progress in the War against COVID-19 is to look at the trends in daily confirmed cases in Florida.  The figure below shows that in the month of April from roughly the time that the governor declared a state-wide lockdown to begin on April 2nd to the time when he began Phase 1 of reopening Florida on May 4th, the number of daily cases decreased steadily.  So Florida’s lockdown did work to limit the number of cases and deaths in Florida.  However, since the state began to reopen, the number of cases has begun to increase again in May.  Some of this increase may be due to increased testing of asymptomatic and mildly symptomatic cases.  But the recent leveling off in death count at 31 per day and the case fatality rate at 4.4% is worrisome.  If you prefer to check progress via the effective reproduction numberR = 1.03, for Florida right now – borderline problematic in terms of renewed infection risk. 

With Universal Studios set to reopen on June 5th and Disney World scheduled to reopen on July 11th, we are especially worried that South American tourists and snow birders entering their winter will be highly tempted to visit Florida.  Thus far only travel from Brazil has been restricted but all of South America is severely infected and travel from there to the USA should be restricted for the next couple of months. 

California COVID-19 Infection Rate is Growing Again

California (CA) had and still has one of the best records in the war against COVID-19 in the USA with less than half the national average infections per capita and just 13% that of New York State.  At the same time its economy has been hard hit so it has little choice except to try to reopen safely.  But since it started reopening some activities earlier this month, its infection rate has crept up.  Its 7-day trailing average daily rate has increased by 25% from 1,723 to 2,170 per day. 

California has published the most detailed demographic information about its confirmed cases and case fatality rate (CFR) which allows us to examine COVID-19 issues and trends in more detail.  The availability of more data confirms some of our major conclusions from our study earlier this month:

  1. Latinos continue to be infected at a higher rate than any other race/ethnicity, but their death rate is just average for the state.  This implies a lower CFR for Latinos (3.8%) than CA in general (5.4%) but after adjusting for age the difference disappears.  It turns out that the Latino population is much younger than average and a lot of young Latinos are getting infected but not suffering very much from COVID-19.
  2. Blacks seem to get infected and die as often as everybody else (CFR of 9.8% vs 8.6% for whites).  However, after breaking out their data by age groups, middle-aged (35–65 yrs old) blacks seem to have twice the CFR of whites while CFR for the very oldest (85+) are about the same for all races and ethnicities (36%).  We suspect poorer health and comorbidities such as obesity and diabetes for many blacks may play a part but additional data will be needed to draw firmer conclusions.
  3. Curiously, the CFR for Californians (purple line in the graph below) overall is not that different than for Europeans such as Italians and Spaniards implying that CA’s hospital system and population health may not be that great. CA’s CFR may be overstated because the actual infection rate may have been and continues to be higher than the number of confirmed cases.  But if so, this undercounting of confirmed cases could also afflict most other countries except South Korea, Australia, and other best in class countries in terms of testing.  South Koreans continue to set the lower benchmarks for CFR (see blue line in the graph below).  

California’s rising case count and increasing effective reproduction rate R = 1.1 is worrisome, but it may be a result of counting more asymptomatic and mildly symptomatic cases as testing protocols are relaxed.  CA has one of the better testing records of states in the US.  It has tested 4.2% of its population about the same as the US average but its tests have returned 5.8% positive cumulatively (better than 11.3% for the US as a whole) and in recent days, its tests have returned below 3% positives.  If it continues to expand its testing it may continue to reopen safely.  If it cannot, it must slow reopening until testing and contact tracing can catch up to return less than 1% positive results.

Sweden’s Failed Experiment

Sweden’s business-as-usual approach in the war against COVID-19 pandemic has been held up by many conservatives such as Senator Rand Paul as a less costly alternative to national lockdowns adopted by most countries around the world.  We have always maintained that Sweden’s laissez-faire or lazy approach (also tried for a short time by the UK and Netherlands, and still followed by devastated Brazil) is inhumane and does not save lives or even economic fortunes.  Moreover relying on “herd immunity” may be wishing thinking — scientific studies show that coronavirus immunity could disappear after 6 months.

While Sweden has always insisted that theirs is not a herd immunity approach they have always hoped that they could achieve herd immunity quickly to end the pandemic in Sweden.  Their latest antibody study showed that just 7.3% of Stockholmers developed COVID-19 antibodies by late April.  Sweden is losing the war on COVID-19 not just because they failed to impose a national lockdown – they failed in basic epidemiology.  They failed in every aspect of the 4T’s required to successfully manage a Pandemic: test, track, treat, and restrict travel.

  1. Testing has been poor – testing 2.1% of their population but only down to 16% positive results while Denmark’s testing returned only 2% positive results (see table below).  Sweden is the worst of all major European countries in testing.  They try to make up for this deficiency with some random serological antibody testing, but the latter is far less reliable than the viral testing they should be doing.  D
  2. Tracking down all potentially infected is tough if their testing is so spotty but they really make little effort at contact tracing.  D.
  3. Treatment yields them their best grade of B.  They have a good medical system that is well prepared to handle the pandemic, but because their testing is so lackadaisical, they often fail to catch the patients in their early stages of infection.  By the time they are hospitalized and tested they are sometimes left with few good treatment options.  Sweden has attributed their poor case fatality rate (CFR) of 12% to outbreaks in senior facilities with many sick, old people.  Poor testing also causes them to miss the asymptomatic and mildly symptomatic cases and artificially lower the denominator and increase the measured CFR.  The figure below plots CFR against patient age and shows that Swedish (purple line) people fared worse than those in Spain, South Korea, and every major country except Italy.  We don’t know how much of this tragic result is due to poor testing and how much is due to delayed treatment.
  4. Travel restrictions get a C grade.  While their voluntary social distancing and travel avoidance, plus some congregation limits (<50) has worked to flatten the curve, the lack of a national lockdown combined with a lack of thorough testing and tracking is causing them to experience thousands of more deaths than their Nordic neighbors: Denmark, Norway, and Finland (see table below).  Sweden has flattened the curve but there is no sign that their pandemic is easing or under control.  Sweden has the highest coronavirus death rate per capita in the world, with an average of 6.1 deaths per million inhabitants a day over the last 7 days. 

Our criticism of Sweden is not that they did not impose a national lockdown — there are countries that have managed their COVID-19 crisis without draconian lockdowns.  But if they chose to leave their country open domestically, they had to implement the other 3Ts: test, track, and treat thoroughly.  Iceland, Norway, and Denmark did not impose stay-at-home orders and left most businesses open.  They all controlled their infection with thorough testing, contact tracing, and early treatment.  Sweden should have done the same and now many top officials in the country are reconsidering their strategy.    

Fatality (CFR)Tests
 Testing PositiveMedian Age
Sweden        3,291     33,188    3,992        39612.0%  20,79816%41.1
Denmark        1,951     11,289       561          975.0%  90,8952%42.3
Norway        1,541        8,340       235          432.8%  42,4194%39.2
Finland        1,186        6,568       306          554.7%  29,8934%43.1
Iceland        5,290        1,804         10          290.6%170,7453%37.5

Update International Travel Ban List Now

Many countries that have been locked down for over a month are now seeing some stabilization and are trying to reopen.  To improve their chances to reopen successfully, they have all ramped up their testing and tracking capabilities and continue to restrict foreign travel.  While the efficacy of International travel bans are debatable, most scientists believe that for countries to successfully manage a domestic test and contact tracing program, it would help to restrict travel from global hotspots to minimize reinfections.  Once a country has established a comprehensive domestic tracking program and controlled community spread, then they could allocate more resources to testing and contact tracing all foreign travelers. 

The current CDC list of restricted countries was last updated on March 14th,  nearly 10 weeks ago, and urgently needs to be updated to include many new hotspots.  Just today, Russia and Brazil overtook many of the European countries that had been suffering as number 2 and number 3 on the list of most infected countries.  Not only do they have a high number of infections and infections per capita but most importantly they have exponentially growing infections with effective reproduction numbers, R >1, and worrisome doubling times.  That means that a high and rapidly growing number of their citizens are getting infected every day.  Countries like Italy, Norway, Switzerland, and Germany can probably go off the list since their R values have fallen significantly below 1 and their newly confirmed cases have been declining for several weeks.  Removing these countries, however, is not as important as adding the highly infected countries to the CDC list that is used to screen hospital patients, air travelers, and other sensitive venues.  An outdated list makes the USA highly vulnerable to reinfection.  This is especially important as the USA reopens tourist spots like Disney World that are travel magnets for South Americans from Brazil, Chile, and Peru who are entering into their high season for flu infections.  Moreover this travel list should be updated based primarily on public health rather than political or economic concerns.  Let’s not repeat the same error we made in February when we were so focused on China that we failed to recognize the hotspots developing in Europe and let infected Europeans into the USA.  

RDoubling time (days)Fatality Rate
USA1,591,991        4,821 94,994        288     1.06506.0%
Russia   308,705        2,116    2,972          20     1.06301.0%
Brazil   293,357        1,382 18,859          89     1.26116.4%
India   112,028             81    3,434            2     1.20143.1%
Peru   104,020        3,160    3,024          92     1.20152.9%
Chile      53,617        2,808       544          28     1.27111.0%
Mexico      54,346           422    5,666          44     1.211410.4%
Pakistan      45,898           208       985            4     1.19152.1%
Bangladesh      26,738           163       386            2     1.25111.4%
Indonesia      19,189             70    1,242            5     1.20166.5%

When Is an Outbreak Controlled?

Many countries around the world are struggling with the question of when and how to reopen the country after lockdown.  Many, including the UK and Germany, have come to rely on a parameter called R or R0 as a benchmark for reopening and staying open.  What makes R so powerful?  In epidemiology, R0 is the pathogen’s basic reproduction number and represents the number of new infections caused, on average, by a single contagious person.  R, or the effective reproduction number (sometimes designated as Re or Rt), will start at R0 and should decline over time as the population gets infected, builds immunity, and mitigation measures are activated. 

R = (1 - P) x R0

where P is the percentage of the population that is immune or out of the pool of susceptible individuals.  If 60% of the population is vaccinated or isolated then only 40% can be infected and R is only 0.4R0.  R0 of the novel coronavirus has been variously estimated at between 1.5 and 3.5, with the WHO currently estimating 2.0 to 2.5.  When R is reduced below one, a contagious person can infect just one other person and the number of newly confirmed cases stabilizes and declines, and the outbreak can be short-circuited.  When R0 is 2.5 the above equation requires that 60% of the population get infected to achieve “herd immunity” to control an outbreak. This does not end the infection which in this example would continue until 88% of the population is infected.  Measuring R0 is therefore very important but estimating its value, while the pandemic is raging, is problematic and highly model or assumption dependent.

As an example of the wide range of estimates possible for R, we look at two models.  One of the more interesting infectious disease forecasting website is EpiForecasts which provides models of the COVID-19 pandemic for hundreds of countries and subnational regions including all the states in the US.  They currently estimate R, the effective reproduction number, for the US at 1.04 (with a 90% confidence range of 0.9 to1.2).  A few states such as New Jersey have R < 1, but most states have R >1 such as Florida at 1.1 so their expectation is that case counts will increase as the states reopen.  Their forecasts appear to be slightly more pessimistic than the widely followed IHME model and others who increased case and death count forecasts after states started to reopen two weeks ago.  A few models, such as Rt Covid-19, are more sanguine and estimate a lower R for the US as a whole (~0.85) and R > 1 for only one state, Minnesota.  Their model suggests that the COVID-19 infection is under control in the US and states are safe to open.  Their model for Florida shows a current estimate of 0.89, increasing slightly and with widening uncertainty after the state reopened recently. 

Given this wide variability in estimating R, with one model saying no and another saying yes, we prefer to go back to the original US recommendation for benchmarking safe reopening strategies.  One of its gating criteria simply requires that states demonstrate 14 days of declining confirmed case count.  By this measure, Florida was one of the first of a handful of states to qualify.  Now two weeks later, Florida wants to move on to phase 2.  The figure below shows that as of May 1st, the state met the criterion for phase 1, and as of May 15th it failed the same criterion to open further.  While we expected this might happen as the state tested more widely, it would seem wiser for the state to proceed more cautiously.  After all, if the outbreak does return, i.e. R > 1, the need to shut down again could cost more in the end.

Kentucky’s COVID-19 Experience

Senator Rand Paul’s criticism of Dr. Fauci earlier this week left the impression that Kentucky solved the Pandemic problem.  On what basis did he conclude that Kentucky “never really reached any sort of pandemic levels… We have less deaths in Kentucky than we have in an average flu season”?

Kentucky has had 7080 cases of COVID-19 — with little evidence that the pandemic has slowed in May.  On a per-capita basis 0.16% of its population — including its senator — has contracted the disease.  326 Kentuckians have died from this disease or more than 73 per million of its citizens.  This compares to the 33 confirmed seasonal flu death in Kentucky this season.  This gives Kentucky a coincident case fatality rate of 4.6%, ~20 times worse than seasonal flu’s 0.24% this year.  The 4.6% measured may or may not be a good estimate given that Kentucky has only tested 2.6% of its population compared to the national average of 3.1%.

If it were a country, Kentucky’s infection rate matches that of Iran, Turkey, Ecuador, and Russia who certainly acknowledge that they are experiencing the Pandemic in a major way.  As a country, Kentucky’s mortality rate matches that of Brazil and Turkey — certainly nothing to crow about.  Both of these are point in time measurements so depending on where each country’s pandemic experience is, the rankings could change over time.  No matter how you slice it though, Kentucky has not escaped the COVID-19 Pandemic.  Now that it has reopened (May 11th) its death count from COVID-19 is likely to more than double by summer.   

Do More Testing — MAGA!

The US President was recently quoted as saying:

“If we did very little testing, we wouldn’t have the most cases.  So, in a way, by doing all of this testing, we make ourselves look bad” 

You have been poorly advised.  The infections are in the country whether we test or not.  Moreover, now that you have reopened the country, too quickly according to some crazy critics, everyone will get infected sooner rather than later.  The infection rate doesn’t really matter much when everyone is infected.  However, if you can test everyone that is infected you can lower the measured case fatality rate.  A lower fatality rate will make American look great again in the eyes of its own citizens and the world.

The US has a measured fatality rate of 6.0%, better than some countries in Europe but definitely worse than some of the countries lauded as best in class for managing their COVID-19 pandemics better than others: for example South Korea, Taiwan, Australia, and Germany.  Each of these countries has surpassed the US in at least one of two important testing metrics: percent testing positive and tests per capita.    

CountryInfectionsDeathsFatality RateInfections
% Testing Positive
U.S.1,290,242 76,8646.0%       3,907       233 23,59717%
Germany   168,655    7,2774.3%       2,015         87 32,8916%
S. Korea     10,810       2562.4%          209           5 12,6662%
Taiwan           429           61.4%            18           0   2,7731%
Australia        6,896         971.4%          270           4 28,3351%

The most important thing is to test widely and efficiently until a country reaches a low enough positive result rate to feel confident that they have sampled the population well.  When only 1% to 2% of all test results return positive then they can feel confident that they have caught not just the most symptomatic cases but also most of the mildly symptomatic and asymptomatic cases in the population.  This gives countries like South Korea, Taiwan, and Australia confidence that if they can isolate all these patients and all those that they came into close contact with, they will have contained the pandemic.  Equally important it gives their citizens confidence to go out to work and shop — “only a couple percent of the population now test hot and only a couple percent of those will die — not so bad.”  Countries that have tested widely and efficiently all have a lower fatality rate than countries that haven’t (see figure below).  This is partly reflective of the fact that countries that have poor testing capacity can only test the most severely ill and most likely to die.  As they ramp up their testing capacity, they can then test and isolate asymptomatic but infectious cases as well and have a chance to stop the pandemic. 

Until we reach that level, an interim metric that measures how widely a country has tested its population is just the number of tests per capita.  For the US testing 8M people and 2.4% of the population seems like a lot but when 17% of those tests had returned positive, it means that we had only probed the tip of the iceberg.  On this metric the US barely makes it into the top 50 countries around the world, far behind the leader Iceland at 15.1% and behind Germany at 3.3% and Australia at 2.8%.  Germany continues to push testing because their tests returned 6% positive, cumulative to date. 

So, Mr. President, I guarantee you that if you tested more widely you can get positive results down to 1%.  Florida just approached 2.5% a couple of days ago.  When this is achieved on a nationwide cumulative to date basis, the US fatality rate will drop below Germany’s 4.3%. (Theirs will always remain higher than ours because their population is much older than ours, but we will never concede this minor point.) The real point is that you will have beaten your nemesis, Angela Merkel, and all the other big silly EU countries as well as China with their ridiculous 5.6% fatality rate — MAGA!

COIVD-19 Demographic Factors

There has been a lot of discussion about race and other demographic differences in communities showing up as higher death rates for example for Blacks and Hispanics.  But it is important to understand the concepts of infection rate, death rate, and mortality rate for a pandemic.  Death rates, the number of fatalities in each subpopulation divided by the number of people in each subpopulation, while stark and headline-grabbing, is not so important in terms of disease understanding and control.  It is a point in time measurement that increases monotonically as a disease progresses from zero to some large scary number.  Different communities may experience the disease at different starting points so it is often meaningless to compare this metric among different communities.  Infection rate, the number of confirmed cases divided by the number of people in each subpopulation is important and indicates how susceptible each group of people may be to a disease.  Fatality rate, the number of deaths in a subpopulation divided by the number of people in each subpopulation that catches the disease is important because it reveals how certain risk factors are causing them to die more often than others who catch the disease.

Let’s look at how these 3 metrics apply to the COVID-19 outbreak in California (CA) as of May 3rd.  The table below shows that the number of confirmed cases for Latinos constitute 47.5% of all confirmed cases in CA.  This might suggest that Latinos are suffering more from the pandemic.  On closer inspection, the percentage of Latinos who die from COVID-19 constitute 34.3% of all deaths in CA.  This suggests that COVID-19 might be less fatal for Latinos.  When we calculate the fatality rate for Latinos it is just 4.1% versus 7.6% for Whites and 5.7% for all Californians (note that this coincident fatality rate may be understated due to differences in timing between diagnosis and death).  But this also would be jumping to the wrong conclusion. 

Race/Ethnicity ​No. Cases% Cases​No. Deaths% Deaths% CA populationFatality Rate
Latino   17,716 ​47.5         720​34.3 ​38.94.1%
White     9,607 ​26.2         730​35.1 ​36.67.6%
Asian     4,320 ​11.8         355​16.8 ​15.48.2%
African American/Black     2,330 ​6.3         216​10.4            6.09.3%
Multi-Race        318 ​0.9             8​0.4 ​2.22.5%
American Indian or Alaska Native          71 ​0.2             7​0.3 ​0.59.9%
Native Hawaiian and other Pacific Islander        416 ​1.1           201.0 ​0.34.8%
Other     2,186             6.0           36​1.7 ​01.6%
Total with data36,9642,0925.7%

The reason that the Latino fatality rate is so low compared to that for Whites is that the median age for Latinos is 27 versus 39 for Whites in CA.  The table below breaks out the CA data into 4 age groups.  You can see that there is a disproportionate number of young Latinos (0-17) that got infected but had zero fatalities that pulled down the fatality rate for the whole ethnic group.  The 0-17 age group had no fatalities – a phenomenon seen in many other countries.  Latino fatalities in other age groups are all consistent with the age dependence we found in every country we studied.  Similarly the apparent higher than average fatality rate for Whites, 7.6%, compared to the state average, 5.7%, can be explained by the higher than average age of Whites in CA.

Asians, especially the young, seem to catch it less often than the population in general (11.8% cases vs 15.4% by population). This may be due to their wider acceptance of mask-wearing in general for disease prevention.  But when they do catch it Asian mortality is higher especially for the 65+ group at 25.9%).  The higher prevalence of multigenerational Asian families may expose more highly vulnerable grandparents to COVID-19 than average.  More data is required to check out this theory.

Blacks seem to catch the disease no more and no less than their share of the population (6.3% of all cases vs 6.0% of the population), unlike in many other cities in the US.  However, they do seem to die more often for every age group, although the statistical significance is somewhat marginal at this point due to small numbers.  Poorer health and higher comorbidities may play a part that could be examined further with additional data. 

Latino7459,979 910.9%4,5111533.4%2,47347619.2%
White1183,670        110.3%2,546742.9%3,26764519.7%
Asian501,892        100.5%1,205443.7%1,16430125.9%
African American      21    949         181.9%    679        365.3%    681      16223.8%
Multi-Race8183            –  0.0%7611.3%50           714.0%
Indian or Native        4      39          25.1%       15           16.7%       13           430.8%
Hawaiian and PI       1     206         10.5%     127          32.4%      82       1619.5%
Other411,120            –  0.0%61050.8%413    317.5%
Total with data98818,038 1330.7%9,7693173.2%8,1431,64220.2%

The lesson here is that early data in a pandemic, especially in terms of death rate differences may turn out to be meaningless.  An infection that starts first in the Black community may seem to produce a higher death rate among Blacks but as it spreads out into other communities, the initial difference becomes less and less significant and could even reverse.  Infection rate differences are important to recognize and attack early since they usually relate to factors that could be controlled such as social distancing, crowd control, mask-wearing, hand washing, and testing availability.  There are other factors that affect infection rates that are more difficult to change such as household numbers, housing density, job requirements, etc. but they could still be adjusted.

Factors that affect fatality rates often cannot be changed or are very difficult to change in the short term: age, gender, comorbidities such as obesity, diabetes, and heart disease.  But knowing the scope of these risk factors can help guide the vulnerable population toward less risky and more sheltered and safer behavior.  At the moment it does not seem that the novel coronavirus respects differences in borders, politics, religion, income, fame, or race. 

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