Sunday, May 31, 2020

How To Not Count COVID-19 Death

In yesterday's post, I described how the analysis of data from CDC web page titled "Excess Deaths Associated with COVID-19" showed that up to 5,310 excess deaths per week in the US are not attributed to COVID-19 (in addition to up to 16,203 deaths per week that were COVID-19 was listed as a cause of death). That prompted me to have a closer look at the detailed data that are available for download from the CDC web site. Here's a graph that shows one of the things I found:
The graph shows the weekly number of "mystery deaths" for six different states. Every death certificate must list a cause of death, and 98.75% of death certificates have a clearly defined cause. But in about 1 of 80 cases, the medical examiner or doctor who fills out the death certificate cannot clearly identify the cause (or causes) of death. In these cases, the death is described by a code for
"symptoms, signs, abnormal results of clinical or other investigative procedures, and ill-defined conditions regarding which no diagnosis classifiable elsewhere is recorded"
This includes a range of codes (R00-R99) that describe symptoms or abnormal lab findings, with code R99 reserved for "Ill-defined and unknown cause of mortality". Note added 6/15/2020: Apparently, the R99 code is also used for "Pending", and some deaths may take several months before the "Pending" classification is changed to a final classification, often in a different category.

The graph above shows that in 2019, these codes were used more or less the same every week of the year, with some week-to-week variations. But for 5 of the 6 states shown, the number of weekly "mystery deaths" increased markedly sometime in February to March, reaching levels that were more than 2 to 5 times higher than in 2019. Here is a look at the raw data for March to May 2020, and the same period in 2019, for the entire USA:
For the US, the "mystery death" numbers more than doubled at the beginning of March, and kept increasing to about 5-fold of the historical level in May (note that data for recent weeks are incomplete, and are likely to increase as more death certificates are submitted to the CDC). Overall, the deaths listed in the "mystery" category R00-R99 account for roughly half of the excess deaths that do not list COVID-19 as a cause of death.

Mystery illness or undiagnosed COVID-19?

The increase in "mystery deaths" is seen in the weeks where the total number of deaths is higher than expected, so all the "mystery deaths" are in addition to "normal" deaths - they are excess deaths. There are several possible explanations for this:
  1. The deaths were caused by COVID-19, but without a positive COVID-19 test. Many of the deaths may have occurred outside of hospitals, or in regions where COVID-19 is only listed as a cause of death if a positive test result has been obtained before death.
  2. The additional "mystery" deaths were not caused by COVID, but instead by one (or possibly more than one) unknown deadly disease.
  3. Added 6/15/2020: The "mystery" deaths are classified as "Pending" and require further investigation. In cases of injury or drug overdose, the R99 code is often used, and changed to the actual cause of deaths in the following weeks or months. Some, but most likely not all, deaths may eventually list COVID-19 as the cause.
It appears quite unlikely that an unknown disease would cause the deaths of more than 2,000 people per week, distributed over many states, without being detected, and that the disease would cause deaths in the same weeks as COVID-19. So the second explanation is very unlikely.

There are, however, multiple factors that support the idea that the "mystery" deaths are indeed undiagnosed COVID-19 deaths:
  • Tests for COVID-19 can give false-negative results, with some machines reported to give incorrect negative results for up to 45% of tests. A negative test result would reduce the likelihood that COVID-19 is listed on the death certificate even if a patient has shown typical symptoms before death.
  • Quite often, COVID-19 patients first experience somewhat milder, unspecific symptoms which get better, before a very sudden turn to severe symptoms, for example a "cytokine storm". The sudden severe symptoms can make it impossible for patients to get medical help in time, especially if they are living alone. Such a death would be likely to classified as a "mystery death".
Overall, it is very likely that the vast majority of excess deaths classified as "mystery deaths" were caused by COVID-19. Historically, about 1.25% of all deaths were "mystery deaths", so that numbers above 1.25% indicate "hidden" COVID-19 deaths. So let's have a look at what percentage of deaths were classified in the R00-R99 "mystery death" category for the US states for the four week period ending 5/16/2020:
38 states, as well as New York City and the District of Columbia, show significantly increased "mystery death" rates. Four states (Vermont, South Dakota, Rhode Island, and Connecticut) show 0% mystery death rates; all of these states except Connecticut reported  no mystery deaths in 2019, either.
The number of COVID-19 cases varies a lot between states. States with a high number of COVID-19 cases would be expected to have a higher number of undiagnosed "mystery" deaths from COVID-19. The graph below shows the ratio of "mystery" deaths to deaths where COVID-19 was reported on the death certificate:
In this graph, I have also color-coded the bars depending on how the state voted in recent elections, using red for Republican states, blue for Democrat states, and purple for states that have senators from both parties, or voted for presidents from different parties in recent elections. There is a strong, but not uniform, bias: Republican states are more likely to have more "mystery" deaths than COVID-19 deaths, while most Democrat-leaning states have more COVID-19 deaths than mystery deaths. Let's have a closer look at some states.


Hawaii shows the highest percentage of mystery deaths. In the CDC data, there was no COVID-19 death listed for Hawaii; however, the state has reported 17 COVID-19 deaths on its website. Hawaii is unusual in having a very low positive rate in COVID-19 tests: never higher than 3%, and around 0.1-0.3% for the last several weeks, with 55,336 tests performed and 652 confirmed cases. Nevertheless, the relatively high number of "mystery" deaths raises red flags, and deserves an explanation.


Tennessee is near the top in both graphs. Here's a detailed look at the reported data from 2020 and 2019:
Relative to 2019, the number of "mystery" deaths more than doubled in April, and showed a 7-fold increase in the second May week. It appears that Tennessee has never reported even half of the COVID-19 deaths as such on the death certificates, and that this fraction has gone down further in recent weeks, while the number of "mystery" deaths has increased.
Tennessee is one of the states that was very eager to "re-open", and has removed  many of the initial restrictions on May 22, including 50% capacity restrictions on restaurants and retail stores.


Like Tennessee, Florida has reported that "mystery" deaths more than doubled in March relatively to last year, and then kept increasing into May:

The reported numbers for COVID-19 deaths in Florida started declining in May, but the number of "mystery deaths" increased at the same time. Florida's governor has been very hesitant to issue a "stay-at-home" order, and has been very eager to re-open the state. There have been multiple reports about the Florida Department of Health trying to suppress information about COVID-19, including new restrictions about what data medical examiners were allowed to release to the public, the omission "snowbird" cases from published numbers, and the firing of the scientist responsible for Florida's COVID-19 database because she refused to manually change data. Florida has relatively high COVID-19 test numbers, but test availability varies widely, with testing being less available in poorer neighborhoods - where infection rates tend to be much higher.

Motive, means, and opportunity to "twist" the data to support the rapid re-opening of Florida all were present. The price, according to the death certificates? About 500 deaths per week. Perhaps the "not elsewhere classified" category is indeed appropriate: none of the other categories lists "sacrifice for the economy" as cause of death.

Saturday, May 30, 2020

Excess Death Counts and COVID-19

How many people really die because of COVID-19 in the US? Reported numbers exceeded 100,000 a couple of days ago, but the reported numbers are subject to errors, biases, and even outright fraud. If someone dies of COVID-19 without ever getting tested, the death will not be included in the COVID-19 statistics in many states. That would cause the reported number of COVID-19 deaths to be lower than the actual number of COVID-19 deaths.

But on the other hand, some states will report "probably" COVID-19 deaths, even if there is no confirmation from a test. Hospitals may be able to get higher payments if an uninsured patient is reported as a COVID-19 patient, which could create an incentive to falsely report COVID-19 cases (although the opposite is true of uninsured patients have enough money to pay the hospital bill, which will be several times higher than what the government pays). Or a patient may be COVID-19 positive, but die from an unrelated disease - and still be counted as a COVID-19 death. All these examples could lead to over-reporting of COVID-19 deaths.

So - is the real number of COVID-19 deaths higher or lower? Or do over- and under-counting simple cancel each other out, and the reported number is correct? To answer this question, we can look at the total number of reported deaths. If COVID-19 really causes additional deaths, that should be reflected. That's how the estimates of annual deaths from influenza are calculated - the actual number of confirmed influenza cases is just a small fraction of actual cases, and "flu deaths" are usually not directly caused by influenza, but rather by weakening a person so that they then die from pneumonia or another "opportunistic" disease.

COVID-19 caused > 20,000 excess deaths

We can start by looking at the CDC web site, which gives us graphs and data links for death statistics. Here's a graph that shows total weekly deaths in the US since last October:
The orange line shows a "maximum expected" number of weekly deaths, based on averages from the previous five years. Towards the end of March, the reported number of deaths was significantly higher than the maximum expected number. The blue bars indicate deaths where COVID-19 was listed as one of the causes; it is easy to see that reported COVID-19 deaths were responsible for most of the excess deaths, but not for all of them. If you look at the original graph on the CDC web site and hover over a bar, you can see the expected and actual death counts:
For the week that ended April 11, the actual number of deaths was 77,759 - that's more than 21,513 more deaths that expected for this week, and increase of more than 25%. For this week, the Johns Hopkins COVID-19 data show fewer than 14,000 reported deaths. The analysis of death certificates (downloaded from here) gives a slightly higher number of 15,333 COVID-19 deaths. Adjusting for incomplete reporting (see the next section) increases that number to 16,203; that leaves an "excess" of 5,310 that were not reported as COVID-19 deaths.

The effect of delayed death certificate processing 

The CDC analysis is based on death certificate data submitted by the states and territories, which arrive with varying delays that can go up to a full year. Therefore, the numbers for the past ~10 weeks are known to be incomplete. The CDC tries to compensate for the not-yet-reported death certificates using elaborate algorithms described on this CDC web page, but it does so in a very conservative way that is much more likely to under-estimate the effect of missing reports. This is quite obvious when comparing the numbers before and after a weekly update; for the week of 4/11, the last weekly update increased the number of deaths by 1,017. Additional increases are very likely to occur in the next few weeks as more data come in, with the largest increases in the more recent weeks. To minimize these distortions, the next section will focus on the 4 weeks from 3/21/2020 to 4/11/2020.

More than 12,000 excess deaths in 4 weeks not reported as COVID-19

The following table shows the expected and actual weekly deaths for the 4-week period that ended on 4/11/2020:
The number of COVID-19 deaths in the table is based on the CDC mortality data downloaded from this CDC web page, and corrected for estimated under-reporting, which increased numbers by 1-5%. Of the 42,348 excess deaths in the 4-week period, only 29,453 deaths certificates list COVID-19 as a cause of death. This leaves 12,895 excess deaths not explicitly linked to COVID-19 for this period. The most likely explanation for these excess deaths is that they were also caused by directly or indirectly by COVID-19. The CDC page can also show graphs about select causes of deaths for 2020:

The graphs shows just a small uptick in deaths from respiratory diseases and cancer, but a larger uptick for dementia and circulatory diseases. The small uptick for respiratory diseases indicates two things: (1) that most COVID-19 deaths that were directly caused by acute respiratory failure were classified as COVID-19 related, and (2) that COVID-19 was not "always and automatically" assumed when people died of respiratory problems. The larger increases in deaths classified as dementia and circulatory diseases are in agreement with what we know about the disease: it primarily kills old people, and many of its most severe effects, like strokes and blood clots, are linked to the circulatory system. The onset of very severe COVID-19 symptoms is often very sudden, and also often seen after a patient seems to recover from the initial symptoms, which can easily be confused with flu or a common cold. Therefore, a diagnosis of dementia or circulatory disease as the cause of death is very plausible, especially when access to COVID-19 tests is limited.

Are there 43% more actual COVID-19 deaths than reported?

It is reasonable to assume that all excess deaths during the height of the COVID-19 epidemic in the US are caused by COVID-19, either directly or indirectly. If that is indeed the case, then the analysis for the 4 week period until 4/11/2020 shown above indicates that the actual number of COVID-19 linked deaths is 43% higher than the reported numbers. If that would apply to the widely noticed landmark of 100,000 COVID-19 deaths, then the actual number of deaths would exceed 143,000.

However, before jumping to a quantitative conclusion, there are several important facts that we need to consider. The increase in COVID-19 testing in recent weeks has reduced the chance that a symptomatic patient cannot get a COVID-19 test, which removes one of the reasons for an incorrect cause on a death certificate (or, more accurately, reduces its importance). Furthermore, the CDC has changed the counting of COVID-19 deaths on 4/14/2020 to include "probable" death; however, it is not clear is this also resulted in a reporting change on death certificates, and not all states in the US follow this practice.

While more tests and better reporting should decrease under-reporting of COVID-19 deaths, other factors may have the opposite effect - but that will be the topic of a different post. Ignoring these factors, we can speculate that the reporting of COVID-19 related deaths has improved in recent weeks. But whatever the current exact number may be, it is very likely that there is still very significant under-reporting of deaths caused by COVID-19. For the 4-week period that ended April 11, the death certificate analysis shows that without any doubt, the number of excess deaths was under-reported my more than one third.

Wednesday, May 20, 2020

Is Age NOT a Risk Factor for COVID-19?

Whenever COVID-19 deaths are plotted by age group, a similar picture emerges, as in this graph for Massachusetts:
It's mostly the older people who are dying. In Massachusetts, the chances of dying of COVID-19 for anyone 80 years or older is about a thousand-fold higher that for anyone aged 20-29. Different regions may show somewhat different numbers, but the overall picture is always the same: the risk of dying from COVID-19 appears to increases with age.

But is age alone really a risk factor for dying from COVID-19? Given graphs like the one above, that almost seems like a crazy question - but it is not. The first hint comes from looking at other health problem of patients who died of COVID-19 had - here is the graph for Massachusetts:

More than 98% of those who died had other health problems like cardiovascular disease, diabetes, hypertension, and so on. Of course, there is a link between age and "underlying conditions" (often called "comorbidities"). But what is really causing more severe COVID-19 outcomes and deaths - age, underlying conditions, or both?

One interesting study that looked at 7,029 COVID-19 cases in adults at least 60 years old looked at exactly this question. The authors concluded:
Age was not a predictor of COVID-19 severity in individuals without comorbidities and structural factors and comorbidities were better predictors of COVID-19 lethality and severity compared to chronological age.
This conclusion was based on modeling the effects of multiple different risk factors, which included various underlying conditions, the number of hospital beds in a community, and "social lag" indexes, "which is a composite of several factors which are measured to estimate social disadvantage and structural inequality based on population census data".

One of the risk factors that the study identified was obesity, which "remained as a significant predictor of mortality even in individuals without other comorbidities"; obesity increased the risk of hospitalization by 70%, and the fatality risk by 37%.  However, obesity does not show a significant increase with age: when looking at a given population, the percentage of obese young people is very similar to the percentage of obese older people. Something does not seem to quite match here!

A study from the Charité university hospital in Berlin helps to understand what is going on.  It looked at 30 COVID-19 patients, and measured their "visceral fat area" with CT scans. Basically, "visceral fat" is belly fat, as opposed to subcutaneous ("under the skin") fat. Visceral fat has been linked to diabetes, cardiovascular disease, and immune system disorders. It generates cytokines, and one of the primary ways to die from COVID-19 is through the effects of a "cytokine storm". The Charité study reports:
An increase in visceral fat area (VFA) by one square decimeter was associated with a 22.53-fold increased risk for ICU treatment and a 16.11-fold increased risk for mechanical ventilation (adjusted for age and sex). 
We'll look at what an increase of "one square decimeter" means below, but take note of the very large risk factors: 22-fold and 16-fold higher risk! A simpler measure that the study also took was the "upper abdominal circumference" - roughly speaking, measuring the waist circumference. They report that each additional centimeter increases the risk of ICU treatment by a factor of 1.13, and the risk of ventilation by a factor of 1.25. The numbers are more impressive if we use inches: one extra inch increases the ICU risk by a factor of 1.36, and the risk of ventilation by a factor of 1.76.

The next thing to look at is how visceral fat increases with age. A study from 2010 shows this graph:
Between the age of 20-29 and 60-69, the amount of visceral fat increases by almost 100 square centimeters - that's one square decimeter. With respect to COVID-19, this increase corresponds to a 22-fold higher risk of ICU treatment in the Charité study.

The study explains that increase in visceral fat with age is linked to weight gain, muscle loss, and re-distribution of fat from arms, legs, and face to a "more central fat deposition".  We know that exercise and physical activity can reduce or prevent weight gain and muscle loss, but it also affects the re-distribution of weight. In other words, exercise and staying active can substantially reduce the age-related increase of visceral fat.

The "typical" development as we get older is that we get less physically active and gain weight. That increases visceral fat, which promotes low-level inflammation and increases the likelihood of multiple diseases, including high blood pressure, cardiovascular disease, diabetes, and others. Each of these diseases itself is a risk factor that can lead to more severe COVID-19 outcomes. As an older person suffers from multiple diseases, independent living can become impossible; the person needs to move to a nursing home or similar long-term care facility. When COVID-19 infections reach a nursing home, the inhabitants are at an extremely high risk of severe disease and death due to the multiple "underlying conditions". This is only exasperated by less time spent outdoor, and the  vitamin D  deficiency that is likely to develop as a result, which has also been linked to more severe COVID-19 outcomes.

Fortunately, the conclusion from the studies I described above is actionable: stay active, exercise, and watch your weight! But before going to a gym, have a close look at the number of COVID-19 cases in your area. Deep breathing (and grunting!) are excellent ways of producing virus-containing aerosols, which could infect you when you breath the aerosols, or touch equipment where droplets landed on. But there are plenty of at-home and outdoors exercise activities - from biking to windsurfing.

Saturday, May 16, 2020

When Singing Kills

In this post, I'll look at what we can learn from a COVID-19 "super spreader" event linked to choir practice in Washington State at the beginning of March. Here is a picture from that summarized what happened:

Of 61 people who attended the 2.5 hour choir practice, 52 got infected with COVID-19. In all likelihood, one person who developed cold-like symptoms three days before the choir practice infected 51 others within two and a half hours. Two of these people died of COVID-19.

A "super sneezer" event?

It is "general knowledge" that COVID-19 primarily spreads through large droplets  - when someone sneezes or coughs directly onto you, or when droplets from his sneezing or coughing land on surfaces that you later touch. I am calling this "general knowledge" because many "authorities" have states this; that includes the CDC and WHO. The "6 feet distance" and the "wash your hands often" rules are based largely on this assumption: large droplets quickly fall to the ground, and don't travel further than a few feet.

However, many scientists have pointed out that COVID-19 is very likely to also spread through aerosols: smaller droplets that can remain airborne for much longer, and travel larger distances. In the "Washington Choir Superspreader Event", it is very likely that a large number of the COVID-19 infections happened through aerosols, and over distances larger than 6 feet. This conclusion is supported by everything we know about aerosol droplet generation and the stability of the new corona virus in such droplets.

But for the sake of argument, let us look if "large droplet" transmission can explain how one person infected 51 others in less than 3 hours. The article from the local health department explains that choir was seated in 6 rows of 20 chairs each, spaced 6-10 inches apart, with a center aisle. Let's assume our "infector", patient 0, was seated somewhere in the middle of a row towards the back. A chair is about 2 feet wide, so there are 2 people sitting next to him on each side - 3 if we are generous. The person sitting in from of him is about 3 feet way, and the two people next to him are also within a 6 ft radius. The person two rows ahead of him is roughly 6 feet away, but we'll also add him. That makes a total of 3+3+3+1 = 10 people within a six-foot radius to the front and sides. Any droplets from coughing and sneezing generally travel forward, but we even if we add three people who sit behind patient 0, we are still at only 13 people within a 6-foot radius. At some point, the choir actually broke into 2 separate sub-groups. If we assume that patient 0 was surrounded by a different subset of people there, that makes 26 people who were within his 6-foot radius.

So to cause all observed 51 infections, patient 0 would have had to "land" droplets on every single one of the people within his 6-foot radius, even the people to his side and behind him. But then, he would also have had to infect a similar number of people during much shorter encounters during the breaks, or when returning the chair. Note that the article stated that "No one reported physical contact between attendees", and that many of the attendees did not eat the snacks offered during the break.

In theory, it is possible that patient 0 did infect 51 others through large droplets - but it seems extremely unlikely. Even if he coughed and sneezed a lot during choir practice, it is hard to see how he would have infected more than the two people sitting next to him; perhaps a couple of people sitting in front of him; and perhaps a few more people during the break.

The simpler explanation: aerosol droplets

 It seems much more plausible that this event is an example of a "superspreader event" where COVID-19 spread primarily through aerosols. As I explained in my last post, scientists have shown that one minute of regular speech can release aerosol droplets with 1,000 - 5,000 virus particles. Loud speech has been shown to generate 5 to 10-fold more droplets. I am not aware of any study that specifically looked at singing, but every choir I have ever seen certainly would qualify for the "loud" category.

During two hours of singing, an average infected person would have released somewhere between 100,000 and half a million virus particles in aerosol droplets that can remain airborne for at least 8-14 minutes, and longer with any air movement. The article mentions "superemitters" who release an order of magnitude more droplets, which would increase the number of virus particles in the air to more than a million. However, the article completely ignores an important study that shows a huge variation in viral load between individuals: some individuals have more than 100 times the average number of virus particles in saliva or throat swabs. That would increase the number of released virus particles to 10 million to 50 million, or more.

The article does not mention the size of the choir practice room, but we can make a guess: if the room was about 70 ft (20 m) wide and long, and 8 ft (2.5 m) high, then the total air volume was 1,000 cubic meters. If we assume even distribution of the virus particles, that gives about 10,000 to 50,000 virus particle per cubic meter. The average person breathes about 0.6 cubic meters of air per hour, so roughly a cubic meter in 2 hours. According to the calculation above, he may have breathed in 10,000 to 50,000 virus particles - almost certainly way more than enough to get infected.

Overall, it seems much more likely that the primary source of transmission in this instance was by aerosol particles. Sure, there is "no proof", but neither is there any proof of large droplet or "fomite" transmission here. But the numbers give a very clear indication what is more likely: aerosol transmission.

The take home lesson: avoid large, loud groups

The more people there are, the more likely it is that someone is infected with COVID-19, and that there is a "superemitter". The more and the louder people talk, sing, or shout, the more virus they set free to search new hosts. If this happens indoors, the aerosol droplets can hang around for a long time; even after settling down on the ground or surfaces, they act like fine dust, and just walking by can put them back in the air. Outdoors, chances are better that aerosol droplets will be moved away quickly - but if the person behind you in the sports stadium is yelling for his team just as you turn around, you may breath in plenty of virus to get infected. The same can happen if you stand downwind of someone on the beach.. or just sunbath. Remember that aerosols travel farther than 6 feet!

Keeping distance still helps, especially outdoors or in well-ventilated areas, since aerosol droplets will be most concentrated closer to the speaker. Facemasks also help, even if they capture only half or three quarters of aerosol droplets; they also keep your "aerosol cloud" closer to you by slowing it down. But you should remember that facemasks generally let a lot of small droplets through - so keep your distance, too!

Note added 6/17/2020: Scientists have been able to obtain the seating chart for the Washington Choir event, and concluded that aerosol transmission is the only possible explanation for the vast majority of infections. The study also outlines the possible effects of increased ventilation, and challenges in avoiding COVID-19 infections in restaurants and indoor events.

Thursday, May 14, 2020

Bars, Beers, and Talking

Wisconsin 's Supreme Court ruled that the governor's "Safer at Home" orders were unlawful and unenforceable, some bars opened up again right away:
What's a bit ironic about this is that just a few days earlier, South Korea had closed bars again, after a 29-year old man infected at least 24 others during his weekend visits of 5 bars and nightclubs. Before that, South Korea had reported fewer than 10 new COVID-19 cases per day for about 2 weeks straight, including several days without any new cases.

Wisconsin's stay-at-home order had been relatively successful at containing COVID-19: when ranking US states by COVID-19 cases per million population, Wisconsin comes in 32nd. But Wisconsin still had more COVID-19 cases and deaths than South Korea, despite having a roughly 9-fold smaller population. Wisconsin is also still reporting about 300 new COVID-19 cases per day.

The mostly young people in the bar clearly are not worried about COVID-19 - they don't wear masks, and they are quite close to each other. Neither did the 29-year old in South Korea; so far, he seems directly or indirectly be responsible for at least 54 known cases. Health departments in South Korea have tried to track down 5,517 people who visited the same clubs so they can be tested for COVID-19.

Let's have a look at how exactly the people in the picture above might get infected by COVID-19, and what the likelihood is. Perhaps a few of them do have parents or grandparents that they would rather not pass the disease to, but they think they are safe "because numbers and changes of getting infected are low".

On first glance, about 300 new cases in a state with a population of almost 6 million does indeed sound like not much. But we know that anyone who carries the virus remains infectious for at least 10 days - that means we have at least 3,000 active cases in Wisconsin, and probably more. Many of these cases will have no or very light symptoms, but still be infectious.

Next, we need to take into account that not everyone who is infected gets tested. Looking at deaths and case numbers, we get a CFR of about 4%, which is at least four times higher than the known "correct" CFR of 1% or less. That gives at least 12,000 active COVID-19 cases in Wisconsin - at least one cheesehead in 500 is infected. There are perhaps 50 people in the bar, so the chances that an infected person is in the bar is about 10%. If we look at 10 open bars with 50 people each, changes that at least one bar is visited by at least one infected person are close to 100%.

 Even given the 10% chance, our young bar goers might still feel safe, because the "stay away from anyone who coughs or sneezes".  Apparently, they do not understand the words "asymptomatic" and "presymptomatic", or perhaps they just have not heard that multiple studies have shown that a very large percentage of COVID-19 infections can be traced to people without apparent symptoms. Or perhaps they simply do not "believe in science" (at least not until they go and visit a doctor).

A new scientific study shines a light on how COVID-19 transmissions in places like bars could happen. The study setup is simple enough to understand even after a couple of beers: speak into a black box; shine a laser light into the box to highlight droplets emitted when speaking; film this with an iPhone; and then count the droplets that can be seen in the video. The study found that one second of speaking produces about 2,600 small droplets. Loud speaking produces more droplets (but who would speak loudly in bars?).

Next, we need to do a little bit of reading and high school math. The reading can tell us how many corona virus particles can be found in saliva - on average, 7 million. The math can tell us the volume of a droplet, and thus how much volume is in all the droplet when speaking. It turns out that 25 seconds of loud speaking produces about 60 to 320 nanoliters of droplets. Multiply the numbers, and you see that one minute of speaking releases droplets with 1,000 to 5,000 virus particles. And that's for the average infected person - some patients have viral titers that are at least 100-fold higher than typical. They would emit at least 100,000 virus particles per minute of speech.

So if you are sitting in a bar for an hour to drink a few beers, a talkative infected person nearby may release anywhere between 30,000 and more than 3 million virus particles into the air. But what happens to the particles? "Classical" theory assumes that most droplets are large, and fall to the ground quickly - but it's largely based on what we can see if someone with a bad cold sneezes. This study estimated that most of the observed droplets were very small, and specifically measured how long they remained airborne. They report "exponential decay times of 8 to 14 minutes"; that means that a substantial fraction of droplets remain airborne for at least that long. Note that this was done in a sealed chamber without any air movement; in moving air, droplets can stay airborne even longer. The bars I have been to generally had some kind of air conditioning or at least fans that moved the air around - and moved any airborne, virus-containing particles around, too.

Unfortunately, we do not know how many virus particles you need to breathe in to get infected. In theory, a single virus particle could be enough, but in reality, the chance that a single virus can create a successful infection is probably small. But with every additional virus you breathe in, chances of infection increase. For various other viruses, fewer than 1,000 virus particles have been shown to cause infections in a high percentage of test subjects. If you are talking face-to-face with someone close to you, this number can easily be reached in a few minutes from interaction between breaths:
Breath interaction (from Villafruela et al, 2016)
For anyone further away, "collecting" many virus particles would depend on the air flow. But if the infected person in the bar is a "super spreader" who releases 100,000 virus particles per minute of speech, many others can easily be infected - which is exactly what happened in South Korea.

The big difference to the bars in Wisconsin is that Wisconsin won't have efficient contact tracing, and that any infection wave originating in bars will be able to spread much further.

Yes, I miss hanging out with friends for a few beers after a windsurf session. Very much so. But you certainly will not find me in a bar anytime soon.

Tuesday, May 12, 2020

COVID-19 Transmission: Questionable Statements

How is COVID-19 transmitted from one person to another? If we know the answer to this question, we can make decisions on how to avoid getting infected.

A lot of people and organizations state that they know a lot about this - but if you actually bother to look at the science in detail, the picture is a lot less clear. Very early on in the COVID-19 epidemic, "experts" told us that the main way that COVID-19 spreads is by "droplets": an infected person coughs or sneezes, which spreads lots of droplets that contain the virus. You then get infected if you catch a droplet, or by touching a surface where a droplet landed.

A lot of the measures aimed at containing COVID-19 are based on this theory: wash your hands often, in case you touched a droplet; stay 6 feet away from others, since droplets don't travel that far; and more. Please don't get me wrong: these are definitely things you should do, because they definitely help to reduce COVID-19 transmissions. But are they sufficient? Considering that we still have almost as many daily new COVID-19 cases in the US as we had a month ago, that seem questionable. What is missing?

Let's look at some of the statements that are made to illustrate that COVID-19 "almost exclusively spread by droplets", as one recent article claimed. I will start with statements by made in a post that has been distributed widely, but I'll use it merely as an example of what is often stated in similar form.

The post makes several dramatic statements about coughs and sneezes:
"A single sneeze releases about 30,000 droplets, with droplets traveling at up to 200 miles per hour. "
"If a person is infected, the droplets in a single cough or sneeze may contain as many as 200,000,000 (two hundred million) virus particles which can all be dispersed into the environment around them."
But while the article is generally good about providing links to underlying science, it does not give a link to the claim that a single cough or sneeze might distribute two hundred million virus particles. I have tried to find any source for this information on Google Scholar and Pubmed without success.

The post also mentions that breath releases droplets:
"A single breath releases 50 - 5000 droplets. Most of these droplets are low velocity and fall to the ground quickly. There are even fewer droplets released through nose-breathing. Importantly, due to the lack of exhalation force with a breath, viral particles from the lower respiratory areas are not expelled."
Again, no source is given. Worse, this statement contains several false statements. The claim that droplets in exhaled breath "fall to the ground quickly" contradicts what is known about droplets in breath. The overwhelming majority of droplets in breaths is very small; one study described that 82% of all droplets in breath are less than 0.5 micrometers in diameter. Typically, droplets smaller than 5-10 micrometers are called "aerosols": due to their small size, they settle very slowly, and can remain airborne for long times. The second false statement is that "viral particles from the lower respiratory area are not expelled". This is contrary to the current understanding that breath aerosol droplets are formed "through fluid film rupture in the respiratory bronchioles in the early stages of inhalation", and the observation that deep exhalation can increase the number of breath droplets five fold.

Next, it gets interesting, when the author writes:
"We don't have a number for SARS-CoV2 yet, but we can use influenza as a guide. Studies have shown that a person infected with influenza can releases up to 33 infectious viral particles per minute. But I'm going to use 20 to keep the math simple."
That's pretty much it: 200 million  virus particles in a cough or sneeze, and just 20 in a breath. So every idiot can see that coughs and sneezes matter a million times more, right?

Not so fast! First of all, this does not really make sense in view of studies that show that many COVID-19 transmissions happen before the first symptoms show up. Especially in countries with strong contact tracing, pre-symptomatic or asymptomatic transmissions account for most of the new infections - and by definition, pre-symptomatic patients do not cough or sneeze.

So let is look at the actual scientific studies here. One study did indeed report up to 20 influenza virus particles in breath. But a second and larger study found much higher viral loads - up to 430 million virus particles when breath was collected for 30 minutes (which amounts to more than a million virus particles per breath). When looking only at patients who neither coughed nor sneezed during the 30 minutes their breath was collected, the maximum number of virus particles collected was still 370,000.  The detection was based on PCR, but the authors also showed that they could actually culture the virus they had collected, so the virus was still "alive".

But it gets better. There is also a study that specifically looked at influenza virus in coughs. This study found a average of only 16 viral copies per cough, and a maximum of about 140. These numbers are actually lower than the number of influenza particles found in breath!

The studies were done in different labs with different equipment, which we have to keep in mind when comparing numbers directly; but both studies found very large variations within the tested patients, with some patients having several orders of magnitude higher viral loads in coughs and breath than others.

Studies have shown that various activities can increase the number of droplets in exhaled breath substantially, often more than 10-fold. These include:
One activity that combines these is singing. Many "superspreader" events have been linked to churches and choirs; some even observed social distancing rules, but still resulted in multiple transmissions. Another activity that leads to deep breathing is heavy work, like in slaughterhouses - another common hotspot for COVID-19 superspreader events.

In view of the scientific knowledge, going to a gym where the goal is to breathe deeply sounds like a great way to get a COVID-19 infection.

There is substantial evidence that aerosol transmission can play a significant role in COVID-19 epidemics. Large, visible "droplets" from coughs and sneezes mostly fall to the ground within a short distance; but smaller droplets can remain in the air much longer. How much this increases the chances of getting infected depends on many factors: Inside or outside? How much air movement is there? Which direction is the air moving? How warm is it? How many people are there? How close are you to the infected person? How infectious is he or she?

Note that the (incomplete) list of factors includes proximity. Even with aerosol transmission, the change of getting infected is much higher if you get close to another person. If you are within a couple of feet from another person, you are "sharing breath" with this person: with every breath, you inhale some of the air he just exhaled. If he is infected, that creates the most direct and efficient way to transmit the virus: directly from his infected lung into your soon-to-be infected lung, with just a very short period in between. I think that this actually may be a, or perhaps the, major way that transmissions happen when people great each other with kisses on the cheek. Sure, a kiss on the cheek will probably transfer some virus particles onto the cheek - but that's not an infection yet. The virus still has to make it from the cheek into the mouth, nose, or eye before it can replicate, and in the mean time, it is subjected to temperatures where it does not survive very long. Even if you touch your check and then your mouth and thereby infect yourself, the virus still needs to get to a tissue where it can multiply, like the back of your throat, or your lungs.

So, what do we make of this all? First of all, you still need to be concerned about transmission by sneezing, coughing, or "fomites" (I like the German word "Schmierinfektion" better).  Just because aerosol transmission can play a role does not mean that the other transmission modes are not important (and perhaps even more important).

But if we know that breathing can create infectious droplets; that speaking, singing, and deep breathing creates more droplets; and small droplets can travel further than 6 feet, we can take that into account when around others. If I had to work in a big office or close to others, I would wear a well-fitting face mask the entire times, and probably have a couple of extras around to replace it from time to time. Fortunately, I can work from home, so the next example may be more relevant: when talking to friends on the beach on a windy day, I'll try to have both of us stand sideways to the wind (and more than 6 feet apart). I certainly don't want you to talk to me when I am downwind of you! I'll also keep my singing down, but that's no big change :-)

Tuesday, May 5, 2020

Containing COVID-19 in the US

It is still possible to contain the COVID-19 epidemic in the US, and to safely re-open without risking many hundreds of thousands of avoidable deaths. Achieving this goal is an enormous undertaking, but it is possible. This post explains how it can be done.

Let me start with a graph that shows a projection of COVID-19 cases and deaths in the US:

The graph shows a COVID-19 model that approximates the epidemic until now: a rapid rise to more than 30,000 confirmed cases per day, and more than 2,000 daily death, followed by a very slow decline in cases and death. It then predicts a rapid rise in daily cases for the next months, to almost 50,000 cases a day, as a result of "re-opening". For the rise shown, the model assumes that many social distancing measures remain in place. The reproduction factor R is assumed to rise to 1.4 from the current value just below 1.0; this is still much less to the R of 4 to 5 early in the epidemic.

The striking feature in the graph is the rapid decline in new cases down to about 8,000 per day at the beginning of June. It is followed by a rapid rise back to more than 40,000 daily cases before a second decline, and then a series of similar peaks that get smaller and smaller.

To get the projected rapid decline in cases, the model assumes that almost the entire population of the US is tested for COVID-19 every 10 days, starting at the beginning of June. Anybody with a positive test result is isolated for 14 days. As shown, the model allows for 15% test failures, which could be a combination of people that are not tested, and false negative test results. The model I used is more realistic than the typical SIRD models commonly used: it tracks each infected person by day since the infection happened, and uses "infection-age" specific infectiousness parameters. It also assumed that anyone who was infected just one or two days ago would give a negative PCR result, and therefore not be isolated. This is why the case counts increase rapidly again after the initial drop.

Let us have a quick look at the number of projected total confirmed cases and death:
Overall, the model run predicts about 2.4 million confirmed cases, and about 240,000 deaths. This is roughly the same number that model runs predicted if the current social distancing restrictions would remain in effect until the end of the year,  and about 460,000 fewer deaths than predicted without population-wide testing.

As I said, the graphs above still assume that many social distancing measures remain in place. Currently, most states that allow restaurants to re-open require that they restrict seating to only 25% or 50% of capacity; however, this makes it hard to impossible for most restaurants to survive. Clearly, the goal has to be to re-open without such restrictions; however, this would result in an increase of the reproduction number to a higher level, for example 2.5. Would regular testing allow for this? Let's have a look:
In the model run shown, almost all restrictions were removed at the beginning of July, so that the reproduction number R increased to 2.5. This resulted in a slight increase in the maximum number of cases in each subsequent test period. To avoid this increase, testing could be done more often. For exampl, if tests would be done every 7 days, then the peak numbers would remain nearly constant over time. Another option would be to keep some measure that reduce transmissions in place, so that R increases only to 2.0 instead of 2.5; this would lead to a steady reduction over time.

The big question is if this level of testing can be achieved. Without a doubt, this would require a tremendous effort. Currently, the US is doing up to 300,000 tests per day; testing the entire population every 10 days would require more than 30 million tests per day, a one hundred fold increase. But until March 10, the US did fewer than 3,000 tests per day, so we have already increased testing capacity 100-fold once; I believe that the US can do this again.

For comparison, let us think back at the Human Genome Project - a major success story for science where the US played a leading role. I was just starting my Ph.D. thesis when the Human Genome Project started, and back then, very few scientists believed that sequencing the human genome would be possible in the projected time frame. But the project was completed years ahead of schedule, and led to major technological breakthroughs. These help us to study and understand the COVID-19 epidemic today, since sequencing a viral genome has become a trivial and extremely fast exercise.

A lot of technology that was developed for the Human Genome Project is very similar to what we need to population-level COVID-19 testing. Many biomedical laboratories have the robotics and PCR machines needed for the tests, and plenty of students and researchers who could help to jump-start the testing. There is a tremendous amount of resources that could be dedicated to this effort on a temporary basis. Considering that we are talking about saving hundreds of thousands of lives, the vast majority of laboratories, researchers, and students would certainly be happy to play their part.

If you take an emotionally detached stance and look at how different countries deal with the COVID-19 epidemic, the observations can be quite fascinating. Countries that have been successful in containing the epidemic have played on their cultural strength: China used drastic control measures; Germany has a scientist as a leader who presented a clear message, and a population that is used to follow rules and regulations; and New Zealand used an interesting combination of such aspects, backed by outstanding science.

Many of the measures that worked elsewhere would not work in the US, where a substantial part of the population values individualism and "freedom" more than anything else. However, a large-scale engineering and technological approach that combines existing science resources and private enterprise fully matches the strengths of the United States.

To make it clear, I think that the "population testing" strategy is just a medium-term strategy, with the primary goal to bring the level of active COVID-19 infections down to a level where measures like contact tracing can be effective; at the current level of 30,000 confirmed COVID-19 infections per day, and probably at least 200,000 infections that go undetected, contact tracing would be somewhere between impossible and ineffective.

Realistically, it seems unlikely that the US government would endorse such a large-scale testing approach, and implement it in an effective way. This is somewhat ironic, since a successful containment by population-scale testing is likely to be the fastest way "back to normal". However, the strategy can be implemented on a smaller scale - on state-by-state levels, or even city-wide levels. Would this require resources that exceed the possibilities of cities or states? Currently, COVID-19 tests run at about $150 each. Testing everyone in the US for a month (three times) at this price would cost $150 billion. That looks like a tremendous amount, but it is much smaller than the various "rescue" packages that the congress has already approved. More importantly, though, the true costs for reagents and machinery are substantially lower than $150 per test - a number below $5 per test is more reasonable. For just a small fraction of the $2 trillion "CARES" act, every person in the US could be tested every 10 days for a year.

There are many non-trivial details in the implementation. Increasing testing capacity 100-fold within a month, as the graphs above assumed, seems quite unlikely; however, the initial rollout could concentrate on the most heavily affected cities and counties, where the impact would be largest. Compliance would be another issue, but one that is solvable: virtually everyone who drives a car in the US has accepted that they'll need to get a drivers license. Testing nearly everyone will require a certain level of enforcement,  but I believe that the vast majority of Americans would agree that saving hundreds of thousands of lives would be worth it.

It's possible. Will it happen?
There is actually an example where this strategy was used successfully on a small scale in the town of Vo in Italy. I started looking into this after reading an article titled "Population-scale testing can suppress the spread of COVID-19".  The article uses a model that in to simplistic, and therefore over-estimates the number of "misses" that the approach allows, but the general idea is a good one.

Monday, May 4, 2020

What 200,000 Daily Cases by June 1 Means

Numerous web sites have mentioned a report by the New York Times that the Trump administration projects an increase in  COVID-19 infections to 200,000 per day by June 1, and an increase in daily COVID-19 deaths to 3,000. The information has been repeated on conservative web sites like the National Review, and on liberal web sites like the Guardian.  Here is what the guardian wrote:
I have not seen the FEMA chart or the CDC models (both of which probably only have seen shared in "top secret" meetings), but it is easy enough to adopt my computer model to give the same numbers:
Basically, the model assumes that the reproduction number R increase to 2.4 because restrictions are lifted. That is substantially less than the R of 5 during the initial phase of the epidemic, but a bit more pessimistic than what I had used in my recent post "The Cost of Making COVID-19 Disappear". But the higher R is needed to get about 200,000 daily cases and 3,000 daily deaths by the end of the months.

Some of you may have noticed that the projected number of cases is about 6-8 times higher than during the last week, while the projected deaths are only 1.5 to 2 times higher.  Looking at the graph above, you can see why: because an increase in deaths always follows the increase in cases with a significant delay - typically about 10 days to two weeks. Another way of looking at this is to compare the number of deaths and cases the US is currently reporting: about 69,000 deaths for 1.2 million cases. All else being equal, that would mean a daily number of 200,000 cases should (eventually) lead to about 69,000 * 200,000 / 1,200,000 = 11,500 daily deaths.

But as the graph above shows, the number of daily cases and deaths is still rapidly increasing at the end of the month. Let's run the model a bit longer, and see what happens:
The number of daily cases will continue to rise to more than 800,000 cases per day before it starts dropping. The number of COVID-19 death is predicted to rise to more than 60,000 per day by the model. Note that the model does not consider the effect of shortages of ICU beds which would lead to even more deaths.

Here is a look at the total predicted number of cases and deaths:
The total number of confirmed cases would exceed 30 million. The total number of deaths would be more than 2 million.

We know that the administration is pushing ahead with "re-opening" plans while being fully aware that the number of deaths will increase to 3,000 per day within a month. Even if the number would stabilize at this level, it would still correspond to 90,000 deaths per month: roughly the combined total death toll of the Korean War and the Vietnam war in a single month.

In all likelihood, though, the daily death toll will increase to significantly higher numbers. The administration knows this, and is pushing ahead with "re-opening" plans anyway. It values "the economy" higher than the life of a million Americans (or two).

Sunday, May 3, 2020

A Tale of Two States

COVID-19 cases yesterday: Nebraska 309, Montana 2. Let's have a closer look at how the two states got there. Here is the graph of cases for Nebraska:

If we look at the blue curve that shows 7-day averages, it's a steady increase in cases. Nebraska was one of the last states to issue a "stay-at-home" order. Governor Ricketts announced the stay-at-home order on April 9. He used very short, simple sentences:
Note that the second rule states "use the six-foot rule as much as possible in the workplace".  The health department issued a somewhat more detailed description that included restaurant closings, but otherwise, businesses in Nebraska were allowed to remain open, even if social distancing was not possible.

Now let's look at Montana:
Montana had a rapidly increasing number until the end of March. Governor Bullock issued two executive orders on March 26 that include 10 pages of detailed restrictions. These included:
  • An order to stay at home "to the greatest extend possible".
  • Prohibition of "all public and private gatherings of any number of people", with very limited exceptions.
  • Prohibition of all non-essential travel, and a restrictive definition of essential travel.
  • Closures of non-essential businesses, with a detailed and restrictive description. For example, "Critical Trades" like Building and Construction were only allowed for "service providers who provide services that are necessary to maintaining the safety, sanitation, and essential operation of residences, Essential Activities, and Essential Businesses and Operations". 
  • A paragraph that the restrictions were enforceable by the Attorney general, county attorneys, health departments, and other local authorities. 
Whereas the Governor of Nebraska was telling citizens that they were "doing a great job at complying with social distancing directives", the Governor of Montana outlined exactly what social distancing measures were expected from individuals and businesses.

At the beginning of April, the two states had a very similar number of COVID-19 cases. The governor of Montana issued strict restrictions and closed all non-essential businesses, which resulted in dramatic drop in new infections; for each of the last 6 days, Montana had between zero and two new COVID-19 cases. When Montana re-opens, its residents can feel reasonably safe.

In contrast, the governor of Nebraska took a "economy-friendly" approach that allowed most businesses to operate. Instead of outlining restrictions and expectations on how citizens should behave, he congratulated them on "doing a great job", and used sentence structures that are perhaps appropriate for toddlers. As a result, the number of new COVID-19 cases increased to  more than 300 per day, and appears to be still increasing rapidly.

Most other US states fall between these two examples. In general, there is a strong correlation between how quickly restrictions were issued, and how strict they were, and the growth or decline of new cases in a state.

Within the next months, it is highly likely that many states will see a dramatic increase in new COVID-19 infections as a result of the "re-opening" of the economy. Any governors that consider issuing new restrictions to reduce transmissions, rather than just "sacrificing the weak", would be well advised to look at the example of Nebraska and Montana. Of course, there are also many international examples of success in containing the COVID-19 epidemic, which include Taiwan, New Zealand, Australia, and Austria; some of these countries have been even more successful than Montana. But Montana is setting a good example for the US.
The idea for this post is based on a article titled "Variation Among states in rate of coronavirus spread", which highlighted the discrepancies between Nebraska and Montana. The article uses a "slope" approach that is similar to what the "Data Trend Model" predictions use.

Saturday, May 2, 2020

COVID-19 Transmissions at Work and Restaurants

In view of the ongoing "re-opening" of the US economy, it is important to understand the risks of COVID-19 transmissions at work places and restaurants. This post looks at studies that describe such transmissions. A critical element in these studies was that they describe cases in cities with intensive contact tracing and relatively low numbers of COVID-19 infections.

Restaurant Transmissions

The first study it titled "COVID-19 Outbreak Associated with Air Conditioning in Restaurant, Guangzhou, China, 2020". It describes the detailed conditions where one infected person infected 9 others. Here is a figure from this study that shows the seating arrangement:
The infected person, A1, infected at least one person on the table he was sitting on, as well as at least one person on each of the neighboring tables. Note that the distance to the people on table C who got infected was about 10 feet - significantly more than the distance of 6 feet that is suggested in the US. The families on table B and C were seated next to the family on table A for a period of about 1 hour each (the article gives exact times in minutes, most likely based on cell phone location data).

It is likely that transmission of COVID-19 happened through aerosols. Very small droplet can remain suspended in air for extended periods of time. The air conditioner next to table C created airflow that moved the virus-laden aerosol droplets around the room.

Work Transmissions

The second study is titled "Coronavirus Disease Outbreak in Call Center, South Korea". It described a cluster of 97 COVID-19 infections in skyscraper. Of these, 94 happened in a call center located on the 11th floor, where 43.5% of the 216 employees were infected. Here is a layout of the office that shows where the infected persons where working:
The transmissions here happened over a period of about two weeks. In theory, it is possible that the infections happened mostly through close contact, for example because the employees also shared elevators. However, face masks are generally used by almost everyone in South Korea when in public, and probably were commonly used during elevator rides, too. Given the distribution of the infections, it seems probable that at least some of the transmissions also happened through aerosol transmissions.

A third study described three different clusters in Singapore of which one was from a work-related conference. This cluster included 7 cases among conference attendees, which later led to 13 known secondary transmissions in France and Malaysia. Some of the transmissions probably happened during a 3-hour dinner where some of the participants share a table; other transmission may have happened during breakout sessions or team-building exercises.

These examples illustrate that restaurants and offices can create substantial risks of COVID-19 infection. It is likely that aerosol transmission can play a major role in the transmission in these settings. The SARS-CoV-2 virus multiplies in the lung, and small virus-laden droplets are formed and exhaled with every breath. In air-conditioned office buildings, the humidity is usually low, which means that the water in exhaled micro-droplet can evaporate within seconds, leaving smaller and lighter "core" particles that can remain airborne for extended periods. Such particles can easily travel distances larger than 6 feet, especially when significant air movement from air conditioning is present, and then infect others.

In shared office spaces, most workers will have no or very limited options to reduce the risk. Increased ventilation can remove aerosol particles quicker, if the ventilation actually replaces the air with fresh air, rather than just re-circulating air. Other options can include staggered shifts, the use of face masks, or work from home, but such options will not always be available, or may have only limited effectiveness.

In contrast, dining in restaurants is often optional, and must be weighed against potential health risks. While the actual risk of dying from a COVID-19 infection for younger people without medical conditions is low, the risk of severe symptoms that require an extended hospital stay is substantial. Many COVID-19 patients have received "surprise" hospitals bill for co-payments, visits from doctors that were not part of the "preferred provider" network of their health insurance, and other charges that were not covered under special "no-copay" COVID-19 rules. Even if covered by an insurance plan that does provide 100% coverage for COVID-19 related health care, there is a significant chance that a test for COVID-19 returns a false-negative result, and that general co-payments and deductibles apply.  One survey of studies found reports of false-negative rates ranging from 2% to 29%. Other studies have shown variability depending on swab type usedwhere the sample was taken; the day after infection that the test was performed; and which machine was used for the test.