COVID-19 Odds

Quantitative analyses on the global coronavirus pandemic

Herd Immunity vs Effective Human Immunity

Classic “herd immunity” is achieved when enough members of a population get infected and acquire natural immunity so that too few uninfected members are left to spread the disease.  The threshold percentage depends on how infectious the disease is and for COVID-19 it is not known but generally believed that 65%-75% of the population needs to develop immunity to stop this pandemic.  For humans, there are two more methods to slow or stop a pandemic: behavior immunity and vaccine immunity.  Governments can convince their citizens, or if necessary mandate, many public health policies that can mitigate the spread of disease.  Keeping your distance, wearing a mask, selective isolation, and improving personal hygiene are things that cattle can’t do but humans can and should do.  People in many countries such as Taiwan, New Zealand, Australia, and Vietnam have been able to control COVID-19 for over a year now without a vaccine or natural immunity.  Even in countries with greater emphasis on personal freedom vs community health, enough segments of the population do follow public health policies and contribute to the overall “effective human immunity” of the population. 

In the USA, behavior immunity has been unreliable but not totally useless.  When people see confirmed cases in the USA reach a horrendous 250,000 per day shortly after New Year more take notice and reach for their masks.  When they see 24M or 7.3% of their family and friends cumulatively get confirmed COVID-19 more may maintain social distance.  When the new administration mandated mask usage at Federal facilities it improves behavior immunity.  Near this level of infection, most people will have known at least someone within their immediate and one removed circle of family and friends that has had a confirmed case.  It is hard to maintain COVID denial when among their 10 closest friends and family and their 10 closest friends (100 people) someone they trust gets COVID-19.  Most people will modify their behavior – improving behavior immunity. 

Moreover, the true level of community infection could be 2 (2.8 is our best guess for USA cumulative to date) to 8 times higher than that reported as many people get asymptomatic and mildly symptomatic COVID-19 that never got tested and confirmed.  Everyone who gets COVID-19 develops certain amount of natural immunity depending on the severity of their case.  Currently the small number of reinfection, ~50 worldwide out of 111M confirmed cases and certain specific studies suggest that natural immunity could be better than 95%.  Adopting more optimal strategies of postponing or only giving one-shot vaccines to those who have had COVID-19 or postponing the second shot will allow us to reach effective human immunity sooner.  Some have suggested that when the cumulative confirmed cases pass 11%, the true level of natural immunity in the community could surpass the 70% needed for COVID-19 herd immunity.  This level was approached (9%) in North Dakota (ND) and South Dakota (SD) by Nov 15th  and Nov 27th, respectively, and daily case counts peaked then.  However, the fact that new cases continue to be reported every day in ND even as 13% of the population has now confirmed COVID suggests that the true level of total cases is not 6.5 times reported but much lower.  Looking at highly infected communities such as Miami-Dade County in FL where 14.5% of the population has had confirmed COVID-19, antibody tests (a convenient but possibly incomplete measure of immunity) show only a 22% cumulative positivity rate, and cases have peaked but not stopped suggesting that the level of hidden cases is probably only 2 times confirmed. 

Nevertheless, we may be closer to achieving effective human immunity than most are forecasting.  In ND, a combination of vaccine (currently 15% at least 1 shot) and natural (currently confirmed 13% and estimated total 35%) immunity could soon end the pandemic even though only 15% of their population is estimated to adhere to CDC guidance for masks and social distancing.  Similarly in Miami-Dade, effective human immunity is approaching 70% (n37%+v10%+b18%).  For the USA as a whole, 8.6%-25% natural immunity currently plus 13% vaccine immunity and 25% behavior immunity may allow the country to achieve effective human immunity by the end of April (n29%+v26%+ b20% – see graph below). 

This optimistic view may be undercut by communities rushing to reopen and removing mitigation measures before the contagion has fallen below critical levels.  The other caveat is that if the more contagious variants take hold in the USA, another surge in cases may occur stretching out the time to effective human immunity.  Even under these more pessimistic scenarios, the USA should achieve effective human immunity by mid-summer if vaccinations proceed at the current 25M people per month.    

Re-opening Schools

The new US administration has made re-opening schools a priority.  There are many benefits to re-opening schools and certainly, re-opening schools are more important than re-opening bars and many other businesses.  But there are many risks as well. 

One of the risks is the susceptibility of kids to COVID-19.  Kids suffer far fewer fatalities and hospitalizations than older adults (although kids could suffer long term ill effects with COVID-19).  The question really comes down to how easily do kids acquire the virus and how easily do they transmit COVID-19 to others and fuel the pandemic. 


 In Florida, most schools and universities reopened in late August 2020.  Since then the number of daily confirmed cases per capita has risen steadily for all age groups.  College and university-aged (18-24yrs) students are most active and mobile and show the highest cases per capita – currently 30% above average.  High school students (14-17yrs old) have always tracked near the average infection rate.  Elementary school student (5-10yrs old) infection started out near 30% to 40% of average but has risen steadily over the last 5 months.  Currently, they are 64% as contagious as the average Floridian, and middle school students are 81% as contagious (see graph below).

 Why have kids become more contagious? 

1.     One explanation is that with school reopening, kids are tested more often.  While testing has increased, the positivity rate has gone up as well reflecting a real increase in community spread.  Over the last 7 weeks, tests have topped out at 100k/day in FL. 

2.     The spread of more contagious variants from the UK, South Africa, and Brazil has increased the rate of transmission, including among kids.  Whether kids are more susceptible is an open question.  FL data suggest that kids may be. 

 Re-opening schools should be done in phases with K-5 grades re-opening first and perhaps high schools not at all until community spread is much lower than it is today.  In Florida, most high schools have re-opened along with most sports and this has exacerbated outbreaks in Florida.  We strongly discourage high contact sports such as high school wrestling that have led to super-spreader events. 

Trump’s Legacy – Half a Million Americans Die of Covid-19

Before noon on January 20th, President Trump will leave his office.  At that time the reported death toll from COVID-19 in the USA will be over 400,000 – the exact number depending on who does the tallying.  Worldmeter will show 412k – real-time, Johns Hopkins will show 402k – lagging by a day, and CDC will show lower – lagging by a couple of days.  All these estimates understate the real toll history will attribute to Trump – over 500k Americans died on his watch.    

COVID-19 death reporting has time lags and other issues.

1.     Accurately assigning the correct cause of death is sometimes more art than science.  There are the underlying cause and the proximate cause issue.  Sometimes COVID-19 starts a chain of events that lead to death many months later from lung, heart, kidney, liver, or diabetes problems that are not uniquely attributable to COVID-19.  The US CDC separately defines confirmed and probable counts and reports both now.  A confirmed case or death is defined by matching confirmatory laboratory evidence for COVID-19.  A probably case is more loosely defined but is now included by most states reporting to the CDC.  There is no time limitation.  (Other countries use different definitions that sometimes make comparisons across jurisdictions difficult.)

2.     Excess deaths, or deaths above normal average year expectations, often exceed the reported COVID-19 deaths implying that undercounting of COVID-19 deaths may be occurring using the direct method.  As of Oct. 15th when reported deaths were 216k, CDC estimated excess death near 299k – 42% more.  

3.     Reported deaths sometimes occur more than a month after the actual date of death  Currently, 60% of all US deaths are reported within 10 days of death but some state (like Florida) and many countries can take more than 2 months to be just 75% complete.   

Our models for the COVID-19 virus infection and death are based on curves that rise quickly after exposure, peak, and then fall off with a long exponential tail.  The virus incubates in the victim’s body and proliferates until 10 days after exposure when the viral load begins to decline in response to the body’s defenses.  Those with a low overall viral load may never see a high enough load to experience any symptoms or request testing.  About 10% of those exposed and get tested, typically around day 5, test positive (the current US weekly positivity rate).  About half of these never develop any symptoms but carry a high enough viral load to infect others for about 10 days after test or 15 days after exposure.  Half of those who test positive will usually experience some symptoms.  Most will stay home and treat themselves with medical guidance.  Some 6% of all positives will get sick enough to go to the hospital – although this has dropped recently to near 3%.  The steady drop since August is due to more kids and young adults being positive not requiring hospitalization, but it could also be due to overcrowding of hospital systems in certain regions like Los Angeles and Arizona.  About 1.5% of all those that tested positive will ultimately die in an average of 14 days from testing and 19 days from exposure.  As noted above, these deaths could take up to 8 weeks to get reported and counted.    

Thus when President Biden is sworn in on Jan 20th there will be:

1.     Deaths that have already occurred before Jan 20th that will get reported over the following 8 weeks (35k). 

2.     There will be a percentage of the 3.4M cases confirmed in the period before Jan 20th that will progress to hospitalizations, ICUs, and deaths that no one will be able to save.  The full accounting will take another eight weeks (69k).

3.     Alternatively, by the end of March the excess death report from the CDC will provide a measure of all deaths to Jan 20th and a portion of deaths to Feb 3rd that should be attributed to Trump’s policies and actions that President Biden could not reverse (140k). 

Whether using the case classification method or the excess death certificate method – the conclusion will be that more than half a million Americans died of COVID-19 under Trump’s watch that no one else could have saved.  Some might argue that every country suffered from the same devastating COVID-19 pandemic – it’s not Trump’s fault.  However, if Trump performed as well as the average government around the world and experienced the same average fatality per capita, only 71k Americans would have died by Jan 20th.  Trump’s gross mismanagement of the pandemic will be a large part of his legacy. 

COVID-19 Vaccine Distribution

COVID-19 continues to rage in the USA.  Over the next 4 weeks, 92k Americans will die due to cases and hospitalizations already in the queue.

Effective vaccines are available to slow the spread but distribution bottlenecks will likely delay herd immunity for many months.  In the meantime, the government has changed its guidance today to permit people 65+ and those with pre-existing conditions to get the vaccine now to reduce hospitalizations and the overall case fatality rate (CFR = deaths/cases).  This makes lots of sense. 

The mRNA vaccines level the playing field for older Americans.  It probably doesn’t reduce your chances of being infected by SARS-CoV-2, but if and when you do, you are more likely to be asymptomatic than without it.  That means you are more likely to survive the infection and your likelihood of dying from COVID-19 could decrease by roughly 95%.  This will reduce the extraordinary demand for hospital and health resources.  In fact, the CFR for all age groups could fall below 2%.  The strong caveat though is that SARS-CoV-2 and its variants will remain highly contagious until 80% of the population is vaccinated and herd immunity is achieved.

Demand for vaccines will outstrip supply for months so I would recommend that everyone who qualifies sign up for the vaccine sooner rather than later and avoid the Florida fiasco.  Moreover, releasing vaccines reserved for second doses means that inventory and distribution management will have to be extremely well-tuned to avoid missing second doses at the recommended times.   This is a well-studied problem in business supply chain and inventory management.  However, given the government’s track record to date, this will not be a slam-dunk.  

COVID-19 Third Wave in Florida

The third wave in Florida has been a little more challenging to forecast for fundamental and political reasons.  The third wave in Florida began with the opening of the school year in September and began to be manifest as increased cases in early October (see figure below). 

Hospitalizations began to rise two weeks later in late October (see figure below) and is now 3.66 times higher headed toward a new record. 

Increased deaths did not manifest itself until early November (refer back to the first figure above).  All this was predictable.  The less predictable part was the longer lag time or slower transmission of the virus from kids to older adults and then to grandparents who are most susceptible to fatal outcomes (see figure below). 

This last transfer did not take place in large numbers until December when the weather cooled, holiday gatherings occurred, and more activities moved indoors in Florida.  The mass inoculation of seniors 65+ that just began, and the rapid spread of the B.1.1.7 variant among the young should keep the median age of infectees younger in this third wave.  The net effect is to lower our expectation of the case fatality rate (CFR = cases/deaths) for this third wave to 1.6% from 2.0% for the second wave. 

The slower than expected rise in reported death counts is also somewhat artificial due to changes in the way Florida reports deaths due to COVID-19 that stretched the COVID-19 death reporting from 2 weeks for the first wave to 2-4 weeks for the second wave to 3-8 weeks for the third wave.  In the figure below, with deaths plotted against actual date, you can see that late November and December counts are still incomplete. 

Recently some deaths from September finally got reported in January.  We believe this is due to the FL Governor’s efforts to suppress reporting of deaths to make the pandemic seem less dangerous and justify his laissez-faire pandemic policies.  Hopefully when the new administration takes office, there will be less motivation to politicize scientific data for the pandemic.

Our current forecast for Florida is that cases will peak in late January, hospitalizations will peak in early February and death counts will peak in late February or early March.  With a combination of natural and acquired immunity (via vaccines), Florida could achieve herd immunity by summer and hopefully, avoid the fourth surge.

COVID-19 Variants in the UK and California

The UK and California (CA) are two very different places with different demographics but they are now closely tied as having two of the hottest COVID-19 outbreaks in the world.  The UK infection rate is currently at 0.73% of its total population over the last 2 weeks, second only to the USA at 0.86%, with CA leading at 1.48%. 

Both the UK and CA have instituted masking and stay-at-home orders with varying degrees of compliance and success so it is actually somewhat surprising that these two regions got so hard hit.  Masking compliance is 60% and 80% respectively in the UK and CA, and social distancing compliance is -30% and -40% respectively in the UK and CA.  This bodes ill for other states and countries that have looser mitigation measures.

The UK’s high infection rate is apparently 80% due to the new variant (B.1.1.7) in the UK that contains the N501Y mutation (also seen in a South Africa variant).  While this new variant does not cause more severe illness, it does spread more readily.  This new variant has now been detected in 18 countries including the USA.  This new variant has now been detected in Colorado but it has probably already spread in several other states.  We suspect that many of the new cases in CA are also due to the new variant, although the USA has done very little detailed genetic testing.  This deficiency coupled with the US government’s reluctance to enact a rigorous quarantine on UK travel to the USA leaves the USA highly vulnerable to this and future mutations of the SARS-Cov-2 virus and further spread of the disease. 

Optimizing COVID-19 Vaccine in Florida

The solution to the COVID-19 pandemic is at hand and it could substantially reduce deaths in Florida and the USA.  Both the Pfizer/BioNTech and Moderna vaccines have proven to be highly effective with generally mild side-effects.  One question is how to get them distributed most efficiently to minimize the future death count.  So far healthcare workers and nursing home residents have been the phase 1 recipients.  The CDC has recommended that frontline essential workers such as first responders, teachers, and grocery workers, and those 75 and over should be next in line.  In Florida Governor DeSantis has opted to make those 70 and older go to the front of this second group with the reasoning that they are much more vulnerable than 20-yrs old frontline workers.  I agree.

The overall risk of a population group should determine its order in the line for vaccines.  This means the risk of infection multiplied by the risk of dying after being infected.  Frontline workers could be ten times more likely to get infected since they interact with more people every day.  However, a 75-yrs old has a 200 times greater case fatality rate (CFR = fatality/cases) than a 25-yrs old, with a CFR of 9.0% versus 0.045%, respectively (see blue line in the figure below).  Thus a 75-yrs old would still be 20 times more at risk overall than a 25-yrs old frontline worker.

Moreover, the third wave that is currently raging in Florida which has thus far focused on the young student population is slowly transferring to older adults just as they did in the second wave this past summer (see figure below).  Large family gatherings for Thanksgiving and Christmas will accelerate this transfer and endanger the older more vulnerable population. 

We see this happening in an alarming way in Sumter County which overlaps most of The Villages.  Cases there have been increasing this month (see figure below) and yesterday 76 out of 112 newly confirmed cases were 65+ yrs old.  As noted above this group has a CFR of 9%. 

It could be a close race between the virus and the vaccine to see how many people in The Villages can be vaccinated and saved before they are infected and killed by the novel coronavirus.  To further optimize the effectiveness of the limited supply of vaccines we recommend that those who have acquired natural immunity go to the back of the line of this second group, and to make sure that as many as possible get their first shot of these two-shot vaccines before anyone gets their second shot. 

COVID-19 Third Wave in Florida

Most COVID-19 infections evolve from exposure to positive tests to hospitalizations to deaths. This well-defined pattern allows us to forecast the pipeline of confirmed cases to hospitalizations to deaths with a fair amount of accuracy. For example Thanksgiving travels and gatherings exposed a large portion of the population to the novel coronavirus causing positive test cases to rise now, 7-10 days afterward.  5-7 days after that the serious cases go to hospitals.  Another week later they result in a favorable discharge or death. 

When the community infection rate is high and the positivity measure (percent of tests returning positive) is high, only the serious cases get tested as in the early days of the pandemic this spring.  The average lag time from cases to deaths was only 5 days and the case fatality rate (CFR = deaths/cases) was also high (see figure above).  As testing availability improved and the positivity rate dropped and more asymptomatic and mildly symptomatic cases were identified, the lag time between cases and deaths increased to 15 days in the second wave.  The median lag time between case date and death date is reported is now close to 20 days as some states such as Florida take up to 4-6 weeks to actually report some deaths.  The longer the lag time the more difficult it is to model CFR and forecast the daily death rate.  The summer peak in cases led to some deaths that were reported in a timely fashion but a large number of cases took many weeks to resolve due to real extended times for treatment but also due to inefficiencies in the reporting process.  When we compare cases to the actual date of death, the relationship becomes much tighter (see figure below).  


The peak in daily death count actually followed the peak in case count by 15 days as did the rise and fall in this second wave.  The potential pitfall in this comparison is that deaths associated with the third wave is barely seen in the data as death counts bottomed at the beginning of November and are just beginning to rise (with the data for the last 5 weeks is still incomplete.  Some COVID deniers use this to say that the actual death count is still flat for the third wave – discounting the reality that it is flat because the count is incomplete.   

Comparing cases to the actual date of death also allows us to measure the CFR better.  During the first wave when little was known about COVID-19 and only severe cases were treated and lots of older patients died the CFR was near 4.5%.  During the second wave, younger and asymptomatic and mildly symptomatic cases were uncovered and the overall CFR dropped to near 2.0%.  The third wave involved even younger patients as schools reopened and the CFR is currently near 1.8%.  CFR also improved over time due to improvements in treatment plans (proning) and therapeutics (remdesivir, dexamethasone, and bamlanivimab).  Some of this improvement though could be reversed if hospitals and health resources in the USA become overwhelmed as they are in certain regions of the country.    

Thus far Florida has fared much better than the rest of the country in this third wave partly because of the Sunshine State’s milder weather and hospitals are only filled to half of the peak this past summer (see figure above).  But the increase in national travel for the holidays and a decrease in temperature in Florida could make the third wave worse than the first two in Florida. 

COVID-19 Vaccines and Infections

Currently, there is a very small number of Americans that have gained immunity from vaccination trials.  The FDA would probably approve the Pfizer vaccine by Dec 10th and the Moderna one by Dec. 20th.  By the end of this year, Pfizer and Moderna would have supplied enough vaccines to permit 20M Americans to have had their first shot.  By early next year, 19M Americans would have gained immunity from these two shot vaccines (taking into account the current estimated 95% effectiveness of these vaccines).  Many people estimate that enough vaccine would be available to vaccinate 25M-30M Americans every month in 2021 subject to logistical and psychological constraints (deep blue area in the graph below).  Thus vaccine “herd immunity threshold = 230M” could be reached in the USA by the end of summer. 

Herd immunity could actually be reached sooner than that.  Currently over 14M Americans have gained immunity from being infected by SARS-Cov-2.  The immunity may not be perfect but seems to be at least 99% effective for 6 months.  We project that by yearend 19.5M Americans will have tested positive for COVID-19 (red area).  Due to testing bottlenecks and scarcity, there is a hidden population of asymptomatic and mildly symptomatic cases that we estimate to be twice as big as confirmed cases for a total of 42M currently immune and 55M immune by yearend (red+green areas).  The total infected has been estimated to be as high as 8x by the CDC or 111M currently (red+green+purple areas).  We consider this to be highly unlikely for the USA as a whole even though antibody surveys for small sections of the USA have ranged from 2x to 20x the confirmed population.  If we adopt our best guess estimate for total immunity, we project that it will exceed the threshold for herd immunity by mid-year and stop exponential growth in the USA.     

The CDC has established guidelines for prioritizing vaccinations among different groups of people (healthcare workers, and residents of long-term care facilities). But they omitted to spell out who in those groups should be vaccinated first.  In fact, we believe that everyone should be tested for antibodies before they are vaccinated.  This would allow scientists to:

1.    optimize the distribution of an initially scarce vaccine to those who really need it,

2.    provide a baseline and periodic retests to measure how effectively these new vaccines are producing antibodies

3.   provide us with detailed measures of the true population of infectees.

Pre-Thanksgiving Dip in COVID-19 Cases

COVID-19 cases in the USA have shown a sharp decrease over the last 8 days causing the 7-day rolling average to peak and rollover (see figure below – red squares).  The question is whether this is measuring a real lasting phenomenon – perhaps attributable to local COVID-19 fires burning out, or to mitigation factors taking hold, or to some temporary factor associated with the Thanksgiving holiday.  The answer is probably a combination of all three that will ultimately be overwhelmed by an increase in Thanksgiving transmission.

Some COVID-19 outbreaks have burned so strongly and for so long (3-4 months) that local “herd immunity” may be acting as a retardant to the fire.  For example, in North Dakota (ND) 10.3% of the population has now been confirmed infected (see table below). 

StateConfirmedTestingEst. PopDeathsDeath perFatality
 Infection %Positive %Infection % million
ND          10.3                23          47          920            1,207            1.2
SD            9.0                24          44          943            1,066            1.2
IA            7.2                19          27       2,400               761            1.0
WI            6.6                15          20       3,307               568            0.9
NE            6.5                17          22          989               511            0.8
UT            6.0                  9          11          868               271            0.4
USA            4.2                  7          15  273,077               825            2.0

Given their low testing rate and associated high positivity rate near 23%, the true underlying infection rate could be 5X to 10X higher than reported (higher positivity rates correspond to a higher hidden population of infectees). This means that ND could have passed the “herd immunity” threshold of 60%-70% estimated by most epidemiologists.  South Dakota (SD) is not far behind at 9.0% confirmed with 24% positivity rate.  Six US states (ND, SD, IA, WI, NE, UT) are already above 6% confirmed infection rate and could be approaching the herd immunity threshold in a few months.  Four of these states (ND, SD, IA, NE) has refused to impose any kind of statewide mitigation measures and avoided testing and thus have a high hidden population of infectees.  Hundreds of counties in the USA could be approaching this threshold.  These states and counties could well reach herd immunity before vaccines become widely available in March.  By then it would be too late for vaccines to save lives already irretrievably lost. 

Letting the virus run wild has come at a great price for the Dakotas.  Both states have now joined the unenviable 0.1% club, that is more than a thousand deaths per million population reached by 10 USA states and only 3 countries in the world: Belgium, San Marino, and Peru.  (For reference the USA as a whole is at #10 in the world with 825 deaths per million.  The USA as a whole is far from herd immunity with just 4.2% of the population confirmed infected and an estimated 15%-20% as the true underlying infection rate.) 

Part of the reason for the recent topping of case counts could be due to the wide range of mitigation measures many counties and states have undertaken recently to flatten the curve and deal with the overwhelming demand for healthcare services (current hospitalizations are 56% higher than ever before in the USA).  These measures include mask mandates (which we view as the cheapest mitigation measure), limitations on assembly, curfews, and business/activity shutdowns.  Many of them could take several weeks to cut transmission and to manifest themselves in the data.  Moreover, many of them are not mandatory and depend on widely varying voluntary compliance.  Given the wide spectrum of responses, it will take some time to sort out which has been effective and which have not.

Finally, part of the reason for the recent dip in cases could also be just a matter of timing.  Many young adults including college students got tested for COVID-19 in the days before Thanksgiving, hoping to get negative results and a pass to go home (see graph above).  This raised the number of tests conducted to a record high of 1.98 million tests in the USA on Nov 21st.  91% of these tests came back negative and gave millions “pass” to travel.  Over the last 8 days, the number of tests dropped to 1.28 million on Nov 29th – much of it due to many Americans taking long weekends off for Thanksgiving.  We expect reported tests, cases, hospitalizations, and deaths to increase again soon. 

The incoming Biden administration must take charge of the pandemic war immediately.  We are forecasting that an additional 74.5k Americans will die over the next 4 weeks due to cases and hospitalization already in the pipeline.  Moreover, every day’s delay over the next 51 days will add 2k-3k to the death toll (this mean >100k lives irretrievably lost before Inauguration Day and vaccine public availability) – an avoidable and unforgivably tragic chapter in American history. 

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