Quantitative analyses on the global coronavirus pandemic

Author: William Ku Page 1 of 8

The Beginnings of a Third Wave

Last month we were concerned that the leveling off of new daily cases in Florida and the USA was only temporary.  Over the last four weeks of steadily increasing daily case counts (see red squares in the figure below), we are increasingly concerned that we are seeing the beginnings of the third wave as temperatures cool and indoor activities resume in northern USA (Wisconsin is especially bad now).  We are also concerned that the pressures to reopen schools for in-person learning, reopen the economy before Election Day, and the increasing numbers of maskless, crowded rallies are exacerbating the normal seasonal rise in cases. 

Some of the increasing cases could be due to improved testing.  After stalling for 2 months testing has improved as schools and businesses reopen and want to keep ahead of increased infections by increasing testing.  This has again picked up an increasing number of asymptomatic and mildly symptomatic cases.  If this were the only reason for the recent increase in cases hospitalizations and death counts would not increase. 

In fact, after bottoming in mid-September, the number of currently hospitalized with COVID-19 in the USA has been rising for the last two weeks (see blue diamonds in the figure below).  As we had pointed out before this is a leading indicator of a future rise in death counts. 

Death counts are currently stuck near 750 per day (blue diamonds in the first figure above) but will rise again right near Election Day – lagging rising cases by 2 to 4 weeks.  This is not a good harbinger for President Trump’s re-election chances.  We had suggested that he ease off on maskless, crowded rallies in September to improve his chances of reducing the death count by November but he had chosen to forge ahead with large risky superspeader events such as the Rose Garden announcement for Amy Barrett in defiance of scientific advice.  Impatience bought him a second wave in June; impatience will have now bought him a third wave. 

President Trump’s COVID-19

President Trump announced that he tested positive for COVDI-19 on October 1st.  Since then at least seven other attendees of a Rose Garden ceremony for Amy Barrett on September 26th have tested positive for the virus.  We wish them all speedy and full recoveries.  However, the prognosis for each of them varies widely depending on their age, gender, and general health. 

The exponential age and gender behavior of COVID-19 patients has remained roughly the same since we first published our version of the graphic below 6 months ago.  Improved testing and identification of asymptomatic and mildly symptomatic cases mostly among younger adults have improved the overall case fatality rate (CFR = deaths/cases), but have not changed the strong exponential age dependence.  Better healthcare treatments in terms of logistics (avoiding bed, equipment, and supply shortages that plagued Italy early on) and the introduction of newer therapeutics such as Remdesivirsteroids, and clonal antibodies have prolonged patient lives and improved survival rates modestly. 

For example, a 50-yrs old female with average health, like the First Lady, would have a CFR of 0.7%.  On the other hand a 74-yrs old male with average health would have a CFR of 13%.  The President, being somewhat overweight with moderately high cholesterol and blood pressure issues would have a worse CFR – perhaps 30 times worse than for his wife.  For a 31-yrs old female of average health like Hope Hicks, her CFR is less than 0.1% similar to that for seasonal flu.  So the range of possible outcomes is extremely wide. 

Hospitalization is a leading indicator of the severity of the disease.  In Florida about a third of all hospitalized COVID-19 patients eventually die.  The risk of hospitalization for the very obese nearly triples that for a person with normal weight.  Currently the President and Chris Christy (with asthma and obesity) are both hospitalized.  

Schools Continue to Spread COVID-19

A couple of weeks ago we pointed out that schools have become the new breeding ground for COVID-19.  More data have allowed us to understand the problem a little better.  While people of all ages can get infected with the novel coronavirus, it seems that the younger the person, the less likely they are to get infected or die from the disease.  Deducing the real underlying susceptibility to the novel coronavirus is not easy given that the measured infection rate depends on how mobile each group is, how compliant each group of people is with mask-wearing, social distancing, and personal hygiene, and how thoroughly each age group is tested for the virus.  With all grades of K-12 back at school or online at roughly the same time in Florida, those in elementary, middle, and high school are 37%, 47%, and 72% as likely as the average Floridian to get infected, respectively.  Teens in high school (14-17 yrs old) have been trending higher while younger children’s infection rate has remained more stable.  Younger children appear to have stronger immune systems than older teens and young adults that protect them against getting infected, and if infected, they seem to put up a stronger fight against the virus.  

Older teens and young adults going to colleges and universities (18-24 yrs old) appeared to have a modestly greater susceptibility than the average Floridian to the novel coronavirus until the last week in August.  Since college reopened and some athletics have restarted, this age group has become nearly three times as susceptible to the novel coronavirus.  We do not believe that they are intrinsically three times more likely to contract the disease, but their increased mobility and their riskier lifestyle choices make them more attractive vectors for the novel coronavirus. 

If schools and universities that have reopened do a good job of testing, contact tracing, and selective isolation of new cases, they should not pose incremental risks to the general population.  However, if they follow the same pattern as we have observed earlier this summer when young adults frequented bars and restaurants and then went home and transmitted the disease to their parents and grandparents, they could start a third wave of new infections. 

Schools are New Hot Spots for COVID-19

Many students have been back to school for a month now and we are seeing new outbreaks of COVID-19 cases among young people in Florida and throughout the USA.  Fortunately, the June to August resurgence of COVID-19 cases among the general population has eased so that the overall case counts in Florida have not increased yet.  As we had pointed out before COVID-19 is far less deadly for children and young adults but their rates of infection may not be all that different.  From the graph below, children younger than 15 seem to be less likely to get infected but since many have been staying home until recently, and as a group they were thought to be less vulnerable and tend to be under-tested,  Thus it is not clear yet what their true infection rate is.  The age group with the highest infection rate is young adults 25-34 who have been most socially active and were largely responsible for the summer surge in deaths as they went to bars and beaches and transmitted the disease to older adults. 

The summer age transfer can be seen in the graph below.  The median age of new cases in Florida decreased from 44 years old in the spring to 33 in late June, and increased back to near 44 in August as the disease spread throughout the state.  Recently as schools reopened and students became more mobile, the median age in Florida has dipped to near 36 years old. 

Schools at all levels of K-12 grades have encountered increased infections as they opened classrooms and campuses to children.  Young kids can get the disease and transmit it but below the age of 14, they seem to be only half as infectious as the general population (infections could be undercounted due to under testing).  Within K-12 ages middle school kids seem more susceptible than elementary school kids but the statistical significance is not very high.  High school kids 14-17 years old appear to be 70% more likely to get COVID-19 than elementary school kids, 5-10 years old.  More detailed data by school district would help us understand the underlying school reopening issues better. 

Young adults aged 15-24 have been tracking higher than the general population all summer even with schools closed, but as colleges reopened in Florida in late August, the infection rate for this age group suddenly increased more than the general population.  This population segment contributes 27% of all new cases in Florida even though it has only 12% of the population.  The pandemic in the USA could be reignited as colleges are pushed to resume in-person classes and large scale contact activities such as football.  Some colleges are well prepared in terms of testing, contact tracing, and selective isolation but many others are not.  If and when they are overwhelmed and send students home or off campus for remote learning, the risk of community transmission could rise.  The median age of new cases after dipping in September could rise again in October as students infect older adults in Florida and the rest of the USA. 

Until the community where the school is located has its outbreaks under control, schools, especially colleges, should reopen remotely.  If colleges chose to reopen for in-person classes, they must exercise extreme care and follow guidelines recommended by this unreleased CDC document.  Unless they do so, reopening can blow up and put the local community and the country at risk. 

Will Florida and USA See Another Surge in COVID-19 cases this Fall?

Daily COVID-19 new cases, hospitalizations, and deaths have been falling for several weeks in Florida along with that for the USA as a whole.  The pandemic in the USA has not burned out and many states in the Midwest are experiencing flare ups.  In Florida, the daily new case count after falling for 6 weeks has just flattened out this week at a level 5 times higher than in May when Florida first tried to reopen (see figure below).  

This has not deterred the governor from doing his second COVID-19 victory tour and encouraging counties to resume reopening, nursing homes to accept visitors, residents to celebrate Labor Day, and schools to reopen for physical classes and team sports. Will an early victory dance and complacency encourage the virus to surge again this fall in Florida and the USA?  

The governor is betting that kids can go to school safely because they are less likely to get infected than adults.  We have shown that this is not true especially given the rebellious nature of teenagers.  A further assumption is that when they do get infected few will die from it.  This is true although the corollary that they will not suffer severe long term health damage is probably not true.  While only 0.02% of kids 17 and under die from COVID-19, 1.2% of these young people do require hospitalization.  Finally, the assumption that child-to-adult transmission is less likely than adult-to-child transmission is controversial

The data show that children can and are getting more infected throughout the country as schools reopen.  In Florida, the earlier resurgence saw thousands of young adults get infected as they celebrated in bars and attended other large gatherings.  The median age of new cases dropped to 33 in June from 45 in April (see figure below).  

As the younger adults transmitted the disease to older adults at home and in the community, the median age increased back to near 44 in August. Now we are seeing the pattern repeat as kids go back to school.  In the first 5 days of September more than a thousand school-age kids in Florida have been infected along with hundreds of college students.  What is not clear yet is whether these younger kids going home to generally younger parents and grandparents will transmit as seriously as the young adults did in earlier.  We are betting that while it will not be as bad it will nevertheless contribute to a second resurgence in hospitalizations and deaths.  Thus we may never experience a real respite from the pandemic as a potential true second wave comes along with seasonal flu this winter.  

A second resurgence or a third peak is still avoidable.  As long as people continue to wear masks, and practice social distancing and good hygiene, the virus spread can be mitigated.  Governments and institutions such as colleges and businesses need to provide easily accessible and timely testing as well as effective contact tracing and selective isolation facilities.  However, if the government claims victory too early again, and continues to send mixed messages about masking, social distancing, and testing, the odds are on the virus’s side. 

COVID-19 Cases and Deaths are Falling in the USA

COVID-19 cases that began to surge in the USA in June, peaked in July, and have continued to ease leading to lower hospitalizations and deaths (see figure below).  While infections continue to erupt in certain parts of the USA, the largest outbreaks in California, Texas, Florida, Georgia, and Arizona have all topped out leading to improving trends for the USA as a whole.  The 7-day rolling average of daily cases has fallen from a high near 70,000 in early August to near 40,000 recently.  The US can continue on this virtuous path if the President stops waffling about masks and tests. 

It is far too early to declare victory because part of the decline in newly confirmed cases is due to a significant reduction in testing (see figure below).  The 7-day rolling average of daily tests peaked 4 weeks ago near 810,000 and has since declined 16% to near 680,000.  It is unclear whether this is being driven by a President that continues to be ambivalent about doing too much testing and/or a CDC that has recently eased its guidance on testing.  Delays in getting test results continue to plague the country.  While the positivity rate has improved from a high near 9% to 6%, it is still higher than the near 4% low reached in early June.  Moreover, since deaths lag daily new cases by 3 to 4 weeks, death counts have just recently topped out near 1,100 per day in early August.  Due to the high number of cases in the pipeline, 21,000 more Americans will almost certainly die over the next 4 weeks

This summer outbreak differs from the spring outbreak in two very important ways.  One is that the case fatality rate (CFR = deaths/cases) is much lower the second time around as more testing produced more asymptomatic and mildly symptomatic cases that do not require hospitalizations.  Thus the CFR for the country as a whole that was 5.2% for cases that resulted in deaths this past winter and spring (to 6/20/20) improved to 1.7% for deaths reported and projected for the period 6/20 to 9/22.  (Note that the CFR for an active pandemic will necessarily be only a rough estimate as many factors that affect the calculation are dynamic.) 

COVID-19US casesUS deathsUS CFRFL cases FL deathsFL CFR
spring/winter2,330,577121,9805.2%93,7963,1443.4%
summer4,708,87881,4071.7%587,3539,4891.6%

 But one interesting question that it raises is whether any of the improvement in CFR is associated with any improvement in techniques or therapeutics used to treat COVID-19 patients.  Careful clinical studies will be required but the early answer seems to be no.  The US numbers are influenced by too many different factors but cases in Florida were less disparate and if we look at the number of hospitalizations compared with deaths it should show how successfully the hospitals were able to cure their patients.  The strong correlation between deaths and hospitalizations in FL is there even after we smooth out the strong weekly reporting cycle by comparing 7-day rolling averages.  The slope of the best fit straight line indicates that 32% of those going to hospitals for COVID-19 end up dying with the summer showing worse above-trend behavior.  (The percentage may be lower due to those who die outside of hospitals.)  We expect that wider availability of Remdesivir, steroids (dexamethasone), convalescent plasma and improved technique may eventually drive this number down.  Until then, vulnerable adults are still well-advised to avoid getting infected and hospitalized.  

 The other important difference is that so far the summer outbreak has avoided general lockdowns that were imposed by scores of countries and 43 US states in the spring and that came with enormous economic and social costs.  As a result of the resurgence, certain states have rolled back some of their more aggressive reopening steps taken in May by restricting select businesses such as bars, indoor dining, gyms, theatres, and other crowded venues.  Some states and numerous cities and counties have mandated mask-wearing in public and closed spaces.  In early August when few of these measures were working, some observers such as Osterholm and Kashkari and the NY Times Editorial Board called for a general lockdown to crush the pandemic.  Many observers now suggest that selective business closures combined with masking, social distancing, and diligent personal hygiene can help to flatten the curve without general lockdowns.  These cost-effective steps have been widely recommended by health organizations such as the WHO and CDC, and business organizations such as the German Institute of Labor Economics and Goldman Sachs Group.  Along with more accurate and timely testing, contact tracing, and selective quarantines, this low-cost approach might convince more businesses, institutions, and individuals that it is possible to reopen the economy safely.  However, this approach does require that the President stop his waffling and mandate mask-wearing and push for accurate and timely testing.  These should have never been politicized in the first place. 

The Villages in Florida Playing with COVID-19 Fire

The Villages is comprised of 17 special purpose Community Development Districts (CDD) for mostly retirees located in Sumter County, 45 miles northwest of Orlando, Florida.  It has consistently ranked as one of the fastest-growing areas in the USA with a current population estimated at 132,420.  The Villages dominate Sumter County which is considered part of The Villages Metropolitan Statistical Area (MSA).  It was largely spared the full force of the pandemic earlier this year, suffering only 363 cases and 17 deaths to July 1st.  Since then the number of cases has quadrupled to 1475 and the number of deaths has increased to 44.  

These growth rates are consistent with the state of Florida (FL) as a whole and slightly better per capita-wise than FL averages.  For example 2.69% of Floridians have contracted the virus while only 1.16% of Sumter County residents have.  Death count per million is 440 for FL and 330 for Sumter County.  It is this latter number that is worrisome because Sumter County has the oldest population in the USA: the median age is 63 yrs compared to 42 yrs for FL.  Just this age difference would make the case fatality rate (CFR=deaths/cases) 9 times higher than for Florida as a whole.  

That means that the CFR for Sumter County could be 5%-10%.  Given the number of cases that have gone to hospitalization – over 100 in the last 4 weeks – the death count could easily double over the next 4 weeks.  What is equally alarming is that Sumter County along with Marion County (which contains some portion of The Villages and is even more infected) residents and officials do not seem to care and carelessly flaunt masking and social distancing rules.  This makes it very likely the virus will continue to thrive in this NW region of central Florida and kill hundreds of seniors unnecessarily. 

Progression of Novel Coronavirus Infections to COVID-19 Deaths or Recoveries

How does someone who gets infected by the novel coronavirus progress to symptoms to diagnosis to hospital and then to death or recovery?  Much about how the virus attacks the human body remains a mystery but we can get some idea of how the typical case progresses by looking at the data that has been collected about the 18 million people that have been diagnosed with COVID-19 around the world. A significant portion of the world’s population, 100+ million, may have already been infected but never developed symptoms strong enough to warrant a diagnosis or treatment.  In the USA, this number may be as high as 20 million with 4.8 million diagnosed cases.  When a person is diagnosed, it may take 3-12 days before symptoms develop if they develop at all. When they do develop symptoms they may ask for a test which can take a few days to return with a result.  If positive they may be asked to quarantine in place at home for 14 days or be admitted to a hospital if the symptoms are severe enough.  The latter are treated in a hospital and if severe enough may progress to ICU and ventilator.  All along this journey some may recover and be discharged from the pool of active patients or they may die.  In the USA, 157 thousand have died while 2.4 million have recovered.  The census of recoveries is clearly undercounted since the number of known active cases in the USA is probably less than 1 million.  The more information we have about the structure of this pipeline the better we can model and forecast the progression of this disease and subsequent outbreaks. 

Once a case is identified we can begin to track its progress through the pipeline.  Single-day counts have a lot of noise and are dominated by the 7-day weekly cycle so we use 7-day rolling averages for all the Florida (FL) data analyzed below.  The figure below shows the correlation between hospitalizations and cases identified 13 days earlier.  Most patients are tested and sent home to quarantine and wait for test results.  If and when their symptoms worsen they are then hospitalized with an average lag time of 13 days.  As many as 25% (=150/600) of the early cases led to hospitalizations when testing was limited to the most severe cases (the cluster at the lower left).  As testing widened a decreasing percentage went to hospitalization in July (brown squares at the upper right) and fell below the average hospitalization rate of 4.7% represented by the best-fit slope.  

Most of the confirmed COVID-19 deaths occur in hospitals so we would expect deaths to correlate well with hospitalizations with a lag.  The best-fit lag is 6 days.  The best-fit slope indicates that 30% of all Floridians who require hospitalization will ultimately die.  This lag time and correlation have not changed much from spring to summer so there seems to be little improvement in therapeutics to improve outcomes.  In fact, July data shows that when the hospitalization rate got high and facilities and resources in counties such as Miami-Dade may have been stretched, death rates increased above trend.    

Deaths also correlate with cases.  Deaths lag case diagnosis by 19 days.  This is now much longer than the average of 9 days that were typically seen at the early stage of infection when tests were only given to those with serious symptoms or who were most likely infected.  With more testing, mild and asymptomatic cases are now identified and symptomatic cases are identified earlier before they need to go to hospitals.  The best-fit slope is the case fatality rate (CFR=deaths/cases) of 1.65%, much better than the roughly 6% (36/600 = cluster of data at the lower left above the trend line) seen at the beginning of the spring outbreak in FL.   

Given this strong correlation, we can then use the daily case counts to forecast the daily death counts that are sure to follow 19 days later.  If we had good age, gender, and comorbidities data we could refine our prediction for the number of patients that will need hospitalization 13 days after diagnosis and the death rate to follow 6 days later.  This is how we forecast the death count over the next 3 weeks for the USA and every state and county in the USA.

The case counts in Florida peaked on 7/17 and we would expect the death count to peak on 8/4.  A plot of new daily hospitalizations peaked on 7/30 and confirms the 8/4 date for the death count peak.     

This is good news for Florida and some of the other Sunbelt states such as Texas, California, and Arizona, but because these peak rates are very high there is little reason to celebrate yet.  In fact, given that some schools are reopening around the country this month at the urging of the President, we need to remain ever vigilant to avoid a fall resurgence of the spring and summer surges.  A fall resurgence could be more problematic as it will overlap with seasonal flu cases that usually begin in October. 

Are Children immune? – Age Dependence of COVID-19

Recent debates about how and when it might be safe to reopen schools for the coming academic year has put the spotlight on whether young adults get infected by the novel coronavirus and how many subsequently die of COVID-19?   We had noted early on in the pandemic that the case fatality rate (CFR=deaths/cases) for COVID-19 is highly skewed against older males.  The average 85+ years old male has >30% chance of dying once they are infected which is 1000 times worse than the <0.03% measured for 17- years old young females (see figure below).  While you hear about the occasional death of a teenager this is out of more than hundreds of thousands of teenagers who have been infected in the USA.  Of course, no one knows the long term damage that could be caused by this pernicious and poorly understood virus so young adults are still cautioned against behaving irresponsibly and tempting fate. 

Moreover, it is important to note that there is no evidence that young adults are not as susceptible to getting infected by the novel coronavirus and spreading the disease to older adults.  Early data seemed to show that a lower percentage of young adults got infected primarily because many of them got mild and asymptomatic cases and testing was limited by supply constraints to older and more vulnerable people.  In the early days, California and the rest of the USA behaved like Spain who seemed to show that kids and young adults were 100 times less likely to get infected than older adults.  After the USA expanded its testing capacity it became clear that young adults are just as likely to get infected.  The modestly lower infection rate that is measured for children is probably due to more asymptomatic young adults who don’t even bother to get tested.  However, scientific studies have shown that asymptomatic and pre-symptomatic infectees can still infect others. 

This why the June resurgence that started out with young adults partying on beaches and in bars was initially viewed optimistically by some governors as the young behaving irresponsibly with little impact on the rest of the country laser-focused on reopening the economy as soon as possible.  They downplayed the possibility that young adults will interact with older adults and inevitably spread it to them with disastrous consequences.  The following graph shows that the median age of new cases in Florida cases dropped from 47 years to 33 years in late June but has since then crept up above the median age of all people in Florida at 42.2 years.  Now Florida and many other states are announcing record-high death rates every day. 

This bodes ill for reopening schools too quickly when the infection in many parts of the country is still raging hot.  For those counties that have active virulent outbreaks such as Miami-Dade, the fifth-largest school system in the USA, the prudent thing to do for students, teachers, and parents is to reopen with virtual classrooms.  Children are not immune to COVID-19, nor are their teachers and parents.  Assuming the current outbreak tops out, do we really want to repeat the June resurgence in September?

Has Miami Solved the COVID-19 Problem?

Ever since the first case of COVID-19 was identified in Miami on March 11th and the first death recorded on March 27th, the number of cases and deaths have increased steadily in Miami-Dade County.  On March 24th, when total case count neared 500, parts of Miami-Dade began to lockdown with most of South Florida locked down by March 30th.  The lockdowns effectively flattened the curve within weeks.  After peaking with an average of 400 new cases per day in mid-April, the number of cases dropped slowly to near 150 per day, Miami-Dade reopened on May 18th.  As it turned out this level of infection was not sufficiently low enough to safely reopen and soon after Memorial Day new cases began to surge again along with the rest of Florida. 

The daily new cases for Miami-Dade (brown squares) track that of the rest of Florida (blue diamonds) very well at about 25%.  Over the last 12 days the 7-day rolling average case number for the rest of Florida has peaked while that for Miami-Dade has continued to rise, albeit at a slower pace.  What is surprising is that the Miami-Dade death count has deviated even more dramatically over the last 10 days – downward rather than up. 

This suggests that the case fatality rate (CFR = deaths/cases) for Miami-Dade has all of a sudden improved dramatically for Miami-Dade versus the rest of Florida.  It is not clear to us why this should be the case.  The strongest driver of CFR is age, and the median age of cases in Miami and the rest of Florida had dropped in June as more young adults ventured out and partied with poor masking or social distancing.  However, the median age has crept back up for both Miami and the rest of Florida over the last 5 weeks.  Other comorbidities and demographic factors do not appear to have changed significantly from spring to summer to justify this improvement in CFR for Miami. 

So either Miami is vastly undercounting their COVID-19 hospitalizations and deaths recently due to abnormally high volume constraints, or they have found a miracle therapeutic that vastly improves survival rates from a May peak of 8% (=16/200) to 0.6% (=15/2600) now.  We are estimating that the true CFR for Miami-Dade is 1.4%, lower than May’s 8% due to wider testing of asymptomatic and mildly symptomatic cases, younger patients, and better therapeutics, but higher than 0.6%.  Death counts will catch up to this estimate over the next few weeks. Moreover, unless Miami-Dade reverses much of its reopening steps to mitigate the spread, both cases and deaths could continue to rise.  Note that the total case count is now 200 times higher than when it last decided to lock down Miami-Dade.    

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