COVID-19 Odds

Quantitative analyses on the global coronavirus pandemic

End of the COVID-19 Nightmare in the USA?

Covid-19 daily cases started rising again about 4 weeks ago signaling the beginning of a fourth wave in the USA.  However, over the last week cases have resumed declining cutting short the fourth wave.  Is this a real indication of light at the end of the tunnel or are we just seeing the headlight of the oncoming train?

42.2% of the USA has been vaccinated with at least one shot to date (green part of the graph below).  This seems to be too low to meet the 70%+ threshold that is generally believed to be the vaccination level needed for herd immunity.  However, we have always asserted that while rigorous herd immunity with vaccines is the most desirable goal, effective human immunity may be reached earlier and allow the USA to flatten the COVID-19 infection curve.  Effective human immunity is a combination of natural immunity gained through infection by the SARS-COV-2 virus, vaccine immunity, and behavior immunity due to citizens rigorously practicing masking, social distancing, and isolation as necessary.

Natural immunity has been acquired by 32.8M Americans that have been confirmed as infected to date (red part of graph above).  A much larger portion of Americans had been exposed to the virus but had asymptomatic or milder cases of COVID-19 who did not get tested because of lack of available and/or timely PCR tests (dark blue part of graph above).  This could have been as large as 8X the confirmed population a year ago during the first wave when the USA was ill-prepared.  Over time, this factor has declined with wider and more timely testing and we suspect it is just 2X confirmed cases now nationwide.  Large studies have confirmed that natural immunity of 80% is likely for adults <65yrs old for at least 5 months.  Several smaller studies have suggested even high levels of protection for longer periods of time.  For modeling purposes, we assume that at least 60% protection is possible for 12 months.  This model suggests that some 5M of the 90M Americans’ natural immunity is now too weak to protect them much.  This group has also lost members because many of them have acquired vaccine immunity. 

Behavior immunity helps to slow the spread of the disease (light blue part of graph above).  Countries such as Taiwan and Vietnam have successfully used only behavior immunity to keep the SARS-CoV-2 at bay for well over a year.  If everyone had masked, socially distanced, and followed all the other public health recommendations of the CDC, the USA would have reached effective human immunity sooner and avoided the fourth surge altogether.  But too many states relaxed mitigation measures too soon after January.  Fortunately, the pace of vaccination doubled from President Biden’s original goal of 100M shots in 100 days to 200M shots and compensated for this rapid relaxation.  We believe that the USA may be reaching effective human immunity soon.  Thousands of new cases will continue to be reported every day but the ability of the virus to spread exponentially will have been curtailed. 

It may be too soon to celebrate because this effective human immunity is soft and require at least 60M Americans to continue to follow public health guidance rigorously.  Over time, this soft human immunity will harden as vaccine immunity grows, even if at a slower pace than April due to vaccine hesitancy. New and more dangerous variants can still emerge and endanger this optimistic forecast, especially if international travel is relaxed too soon while the number of daily cases globally is still rising from surges in India, Brazil, and Turkey.   

Why Are So Many Seniors in FL Still Getting COVID-19?

Covid-19 mRNA vaccines work very well in real life.  But as more data are analyzed it appears that certain groups of people such as seniors (65+) do not benefit as much from the vaccine. 

We have been tracking the vaccine’s real-life efficacy through Florida’s Seniors First program to vaccinate everyone over 65 years old first.  As of April 19th, 3.6M seniors or 80% have been vaccinated with 2.9M (64%) completing the two-dose regime.  The pace of senior vaccinations has slowed recently and this may be linked to the plateau and now rise in relative infection for seniors (see figure below). 

There are several possible explanations for this observed phenomenon:

1.     Vaccine hesitancy expressed by 27% of Americans in recent polling,  Note that 80% of Florida seniors have already gotten their shot so polling answers may be more political posturing rather than reality.  Nevertheless, at some point before 100%, we will reach seniors who resist the vaccine, and improvement in relative infectious of seniors will end. 

2.     Weaker vaccine protection for seniors.  While mRNA vaccines are near 95% effective and people who are fully vaccinated have only a 5% chance of getting COVID-19 on average, people over 65 are less protected and may have as high as 39% chance of getting infected – near 8 times higher than average.  JnJ vaccine provides less protection for everyone.  Seniors typically have more comorbidities such as weakened immune systems and this may be one reason for their weaker protection.  As the rest of the state and country get vaccinated relative infection rates for seniors could increase more. 

3.     Premature relaxation of precautions after vaccination, especially in the 65-74 yrs old that are mobile.  Those vaccinated who drop masking and social distancing (which combined may be 90% effective) could reduce their overall protection against the virus.

4.     Vaccine effectiveness is believed to be 90% after 6-mo in general for mRNA vaccines, but this may not be true for seniors who may have shorter protection.  Seniors may require more frequent booster shots. 

5.     New and more contagious variants spreading now though Florida are not believed to escape mRNA vaccine clutches, but current vaccines may provide less protection against the new variants and may need to be re-tuned.

All of these factors suggest that it would be prudent for seniors to continue to follow good public health advise for masking, social distancing, and travel.  International travel to 80% of the world is discouraged by the US state department especially with the pandemic raging to record highs globally led by surges in India, Brazil, Turkey, and other hotspots around the world.

Vaccine Progress in Florida and the USA

The good news is that there are now 3 approved COVID-19 vaccines in the USA with more than enough doses to allow all American adults to be vaccine eligible by May 1st.  Two of the vaccines, Moderna and Pfizer-BioNTech, have already proven to be very effective in the field.  These are two-dose vaccines that can take 6 weeks to achieve full protection.  One way to track real-life efficacy is through Florida’s Seniors First program to vaccinate everyone over 65 first.  As of March 13th, 2.93M seniors or 65% have been vaccinated with 1.75M (39%) completing the two-dose regime.  If the vaccine is effective, the number of daily cases, hospitalizations, and deaths should all come down. 

The graph below tracks the relative susceptibility of Floridians by age to SARS-CoV-2 infections.  Seniors have always been more careful to mask-up and social distance since the first COVID-19 cases appeared in Florida and killed hundreds of seniors last spring.  Moreover, the oldest seniors (85+) have been the least mobile and thus least likely to spread the virus.  After rising slightly post year-end holiday gatherings that increased community transmission, relative infection rate (i.e. number of cases per capital for the age group divided by the number of cases per capita for the whole population) has steadily declined over the last 4 weeks from mid-February to mid-March for all seniors.  We are forecasting that these relative infection rates will continue to decline steadily for another 4 weeks as the number of fully vaccinated seniors approach 3.2M or 70% of the group population. After that, we believe that the rate of decline will slow and will run up against a stubborn core group of people refusing vaccines (estimated to be 27%)

This steady decline in senior susceptibility to COVID-19 will positively impact the overall case fatality rate (CFR = deaths/cases).  CFR has decreased from 2.5% in the first wave to 2.0% for the second wave to 1.5% for the third wave in FL.  We believe this will decrease below 1% soon as the median age of new cases falls further below the current value of 37 years old. 

This however does not mean that the virus will no longer be a threat.  The bad news is that the relative susceptibility of kids to SARS-CoV-2 has been increasing since school reopened in FL last year.  The trend appears to have worsened with the spread of the new and more contagious variants this year.  It could be several months before any vaccine is approved for kids under 16.  In the meantime, schools can reopen but it is important that teachers and staff get vaccinated, facilities get upgraded (e.g. ventilation), and masking and social distancing be enforced to mitigate the spread of the disease in schools. 

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. 

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