Coronavirus:do lock-down orders work?

Given the world-wide experience with coronavirus so far, it is reasonable to ask if the common government response of lock-down orders worked. There is little question that the concept of lock-downs has a logical appeal to it, in that it theoretically deprives the virus of the means of spreading. Obviously, the virus has continued to spread.

A distinction must be made between intent and reality. A fundamental issue is what is the intent of a lock-down order, specifically one that affects a large, diverse area with heterogeneous coronavirus exposure. Is the purpose to "flatten the curve," "protect the vulnerable," "stop the spread," "save one life," and so on? It does not appear, from day to day, that the rationale is consistent and therefore the criteria by which to assess the effectiveness of lock-downs are protean. It's hard to say if lock-downs work if it is unclear why we are doing them. More importantly however is the distinction between the theory and practice. The lock-downs of theory are not possible in real life, therefore it is unreasonable to expect lock-downs to deliver their theoretical benefits. The experience of New York seems to be that lock-down orders are not effective because of the dynamics of viral spread and the impracticality of implementing an effective order in that location. The answer to the question "do lock-downs work?" is therefore"no one knows because lock-downs are impractical." This implies that the answer to the more relevant question "Do lock-down orders work?" is "No."

At a certain point, interventions to slow or stop the spread of coronavirus hit the point of diminishing returns, to the point at which the marginal benefit is not worth the associated undesirable consequences. If we were to list all of the theoretical interventions that might affect the spread of coronavirus, the list would probably begin with frequent hand washing, covering coughs, and wearing masks. The middle of this spectrum might include keeping six foot distance from others in public places, sanitizing frequently touched objects in public places and closing schools. At the low yield end would be discouraging people from using words that the contain the letter "p" because they may result in aerosolizing more virus than words with less aspirated phonation. Lock-down orders appear to fall somewhere after the middle portion of this spectrum. This is largely a result of their marginal benefits and significant costs. One may speculate as to the marginal benefit of prohibiting the sale of "non-essential" items and preventing families from being in otherwise empty parks.  A relevant question for this consideration is "Are shutdown orders worth it? Again, with respect to the experiences in such places as Italy and New York, the answer appears to be "not really."

The perceived benefits of lock-down orders may be undone by or frustrated by conflicting policies. The same may said of exacerbations of their costs. The most obvious example is the decision by New York to require nursing homes to admit "stable" coronavirus patients. The rationale for this decision is unobvious, because whether or not a person is stable is a separate consideration from whether or not they are infectious. This illustrates another weakness of lock-down orders: they are subject to vitiation by other governmental decisions. A relevant question in this regard is "Are the beneficial effects of shut-down orders durable in the setting of other interventions?" The answer is apparently "Not always."

The cost/benefit considerations of shut-down orders requires consideration of their adverse consequences. The economic consequences are obvious; less so are the psychological and paradoxically the medical down-sides. It does not take much of the latter to tip the risk/benefit calculation away from government mandated lock-downs as a beneficial intervention.

A significant weakness of lock-down orders, obvious from the outset, is that they are un-focused. They are inelegant and largely uncontrollable interventions that  produce positive and negative results capriciously. They are justified by fallacies and superstition as much as by science, and among their many drawbacks are significant opportunity costs. More effective interventions may be foregone to maintain the otherwise illusory project of keeping people away from each other. One such foregone intervention is the opposite of the New York policy mentioned above. Rather than pretending to isolate everybody, it would have made more sense to actually isolate nursing home residents. It would make much more sense to thoughtfully classify persons as to their risk of not only contracting the infection, but also of experiencing a bad outcome from it, and employ more focused interventions accordingly.

This is mostly hind-sight, and it it may be worthwhile to consider why government-mandated lock-downs seemed reasonable when they were implemented. One reason was because of the uncertainty accompanying the spread of the virus. Much of this uncertainty persists, such as what is the actual prevalence, duration of infectivity, and case fatality rate; do infected people become immune, what are the virulence factors, etc. Couple these with alarming observations such as the experience in Italy and the the contrasting one in Taiwan and it becomes unclear what the correct course would be. The early part of the pandemic was also complicated by distracting issues: the availability and usefulness of ventilators, the controversies surrounding choloroquine and hydroxycholoroquine, the availability and effect of testing, and not insignificantly the huge uncertainty regarding the expected number of cases and deaths. Given this uncertainty, an initial resort to lock-downs was not unreasonable. Now that we have a couple of months of experience, the evidence that they had a significant positive impact is mostly speculative; there is no hard evidence that places with strict lock-downs fared any better than those with less restrictive interventions; in fact an argument can be made to the contrary. This is possibly a reflection of the overly general and indiscriminate nature of lock-down orders; they do not account for the factors that distinguish Taiwan from Italy or Oregon from New Jersey. This makes it only more ridiculous to ignore these distinctions and substitute others such as those between essential and non-essential, or between lottery tickets and garden seeds. Lock-down orders were not unreasonable at the time, but they become more so the longer they persist. Lock-downs in the abstract seem to make sense, lock-downs in reality do not work, at least it would seem, well enough to justify the enormous destruction they cause. Lock-downs may work if they could be efficiently implemented, but because they can't lockdown orders do not work. They do not control spread of the virus, limit mortality, or prevent the use of medical resources, except to an almost trivial degree.

Coronavirus: A modest proposal

As mentioned in previous posts the practice of changing the way that coronavirus cases and deaths are counted makes it difficult, if not impossible to track trends in the course of the pandemic. These distortions are made even more prominent by creating incentives to increase COVID diagnoses, as for example by differential reimbursement for treating COVID cases. As mentioned previously, there may be rationales that favor erring on the side of inclusiveness versus erring on the side of certainty, but the fact remains in either case that the process is one that is friendly to error.

It would be helpful if the agencies responsible for coronavirus record-keeping would make a couple of very basic accommodations:

1. Report separately those diagnoses that are supported by PCR testing, those that are supported by antibody testing, and those that are supported by neither.

2. Report separately those who were diagnosed with COVID and subsequently hospitalized, and those for whom the sequence was the other way around.

3. Report those who have more than one coronavirus test, with the result pattern; e.g. negative-positive, positive-negative, negative-positive-negative, etc.

4. For those admitted to the hospital after diagnosis, report the amount of time that elapsed between these events.

5. Report suspected hospital-acquired infections.

6. Report positive cases that were not associated with a documented fever.

7. Report cases according to whether patients continue to work outside of the home, i.e. in grocery stores, hospitals, etc.

Coronavirus: Speculation

Does the severity of COVID-19 in the average infected person decrease as the epidemic begins to wane? Daniel Defoe's Journal of the plague year passed along this observation of the resolution of the Great Plague of London in 1665:

"...and you will see many more people recover than used to do; for though a vast multitude are now everywhere infected, and as many every day fall sick, yet there will not so many die as there did, for the malignity of the distemper is abated'"

Now allowing for the fact that Defoe's work was a fictionalized account, and that the disease in question was a bacterial plague, one may nonetheless wonder if disease severity declines as an epidemic or pandemic runs its course. 

Quantifying disease severity is tricky, since there are no reliable, or universally applicable criteria upon which to make such measurements. Patient deaths is an imperfect measure since people may be infected at the peak of the contagion but die near the end. One may assume that the more severely ill patients are more likely to be hospitalized, and this may suggest one surrogate by which we can examine the issue. Here is a chart of the ratio of daily hospitalizations to daily diagnoses in Colorado during the month of April:

It is easy see that the chart tends downward, and this is consistent with a hypothesis that disease severity declines as the epidemic progresses, or begins to resolve. Obviously however, many things could account for the observation. It may be that:

1. more people who are less affected are being tested;
2. the criteria for hospital admission has changed in favor of admitting those who are less ill;
3. people who had been diagnosed on one day might not be admitted to the hospital until several days later;
4. there are anomalies in data collection or reporting;
5. testing is more widespread, encompassing more than those who were initially very sick and who met the original criteria for testing;
6. Other things...

It may also be the case that the effect contemplated above is real. The change in magnitude represents an 80% decrease from April 1 through the present. That is a large change to be accounted for by one or two factors. If the effect is real, it might suggest:

1. that COVID-19 is more widespread and less virulent;
2. that SARS cov-2 is becoming less virulent;
3. that environmental factors are influencing the virulence of the virus

Coronavirus: Interim summary II

There is a significant amount of information and data regarding the world-wide coronavirus pandemic that has accrued over the past 3 months. This permits some interim observations and speculations:

1. The coronavirus is worse than a bad flu. The mortality in various locations and wide spectrum of disease does not permit honest comparison with seasonal flu, or even some of the more recent pandemics such as the 2009 H1N1 flu. The experience with influenza includes experience with numerous vaccines, an understanding of virulence factors, and at least some immunity protection from prior infection with related strains.

2. Paradoxically, coronavirus does not spread easily. The numbers of infected people in varied populations is low, with no sizable population yet above 2% diagnosed with infection. The model of infection in which an infected person encounters an uninfected one and this is associated with a high probability of transmitting the virus is overly simplistic. A more reasonable model treats transmission as analogous to a key fitting in a lock, with a number of competing factors promoting and inhibiting transmission at any one time. These factors are time and environment-dependent. Given favorable conditions, the virus spreads rapidly; given unfavorable ones, it wanes. This is consistent with the experience of SARS and MERS.

3. One of the great unexplained questions arising from the pandemic is the huge variance in death rates, even without medical system depletion, and in the presence of extreme government-imposed limitations on activity. This, as above may be understood with the key and lock analogy. There is no single explanation for the differences in attributed deaths-to-diagnoses ranging between more than 13% in Italy and 2% in Japan or 3% in Germany. The same is true for the 7.6 percent rate reported for NewYork and the 2.5% rate in Texas. Whether coronavirus kills a particular patient depends on a constellation of conditions that happen to be very unfavorable in New York and Italy. One possible factor, although not sufficient to explain the entire phenomenon, is that New York is doing something that increases the risk of infection among those most likely to die from it, like admitting patients known to be infected to nursing homes.

4. The haphazard approach to determining which data are significant and for what purposes will prove to be a missed opportunity. One may wonder what some of the downstream effects are. For example, there are currently cancer therapy trials ongoing in which the endpoints are death. What becomes of the carefully managed data in these trials if a death is presumed to be due to coronavirus?

5. There is no guarantee that there will ever be a vaccine to protect against COVID-19. Decisions that assume the contrary are neither competent nor serious.

6. Likewise, assumptions about the utility of "testing" are of unclear validity. Different tests will have different false negative and false positive rates. It is possible that there may be cross-reactivity between SARS cov-2 antibodies and antibodies produced by previous, less virulent coronaviruses. There is the practical problem of a person contracting infection the day after testing negative. There is also an issue with a rare but not insignificant pattern of positive-negative-positive testing. What to do with the last test result? There are assumptions, but no proof that a person who has a negative coronavirus test is not infectious; is this assumption accurate? Is it true for everyone? Most people?

7. Data that would be useful, and questions that occur:
     - How many people who are put on a mechanical ventilator die before hospital discharge?
     - Is there a post-coronavirus syndrome, possibly affecting heart muscle function, causing lung scarring or affecting the kidneys or bone marrow?
     - Do abandoned therapies such as activated protein C, that were previously used in treating sepsis have a role in treating COVID-19?
    - What percentage of people in multi-person households test positive for the virus?
    - Is high concentrations of inhaled oxygen detrimental to the lungs of COVID-19 patients?
    - Are the risk factors for acquiring infection different than those for severe disease?
    - Do government mandates and forcible closures have a significant impact beyond that produced by providing reliable advice and letting people use common sense?
    - Does the severity of disease decrease as the number of new infections tapers off?

8. Although it is not claimed that there is a phenomenon that produces a feed-back effect that influences spread and mortality of the virus, as contemplated in the post "What if...?", the virus appears to behave as though there were. Such a phenomenon might explain not only the relatively low numbers of infections (as was also true with SARS and MERS) but also the stark differences in transmissibility and mortality, the fluctuations in the daily new case counts, etc. It might also address the inquiry that may have set off the whole episode: why don't bats that are infected with coronavirus get sick?

9. So, does social distancing work? The evidence would seem to indicate that the answer is "a little." The experiences in "hot spots" like New York and Italy indicate either that the virus is more resilient than thought and persists for more than a couple of exposures, or that it is not possible to enact social distancing measures strict enough to have a dramatic effect, or perhaps both. This conclusion takes into account the experiences in South Korea and Taiwan who do have social distancing measures, but which do not include the types of isolation that would prevent most transmissions. Social distancing decreases the likelihood of transmissions across the board, but there are other factors that also have large effects, both positive and negative, on disease spread.

 

Coronavirus: Models, data and policy

It may be useful to review how we arrived in our present situation regarding the coronavirus. The decision to institute shutdown orders and stringent social distancing was based on a model constructed before there was significant experience with COVID-19. That model or rather those classes of models were revised several times. It is reasonable to ask, now with more than two months experience with COVID-9, whether those models are useful, or if they even were.

As mentioned previously, policy decisions are justified by reference to some hypothetical number of lives saved. This is a pointless exercise for several reasons. First, it is not a reference to lives saved exactly, it is a reference to lives that may be saved from a particular cause of death. It provides no guidance for lives that may be lost from other causes, including those that may be affected by interventions meant to slow the spread of coronavirus. Secondly, it bears remembering that the rationale behind "flattening the curve" was not to prevent people dying of coronavirus, it was meant to minimize the number of people who may die from lack of access to healthcare whether or not they have coronavirus. Thirdly the specific interventions imposed were based on striking estimates of deaths, 3 million in the United States and 500,000 in the United Kingdom if nothing were done. Certainly, if that estimate had been 10,000 deaths in the United States, or fewer than the number of deaths attributed to the 2009 H1N1 pandemic, we would have expected the response, and suite of interventions to be similar to those of eleven years ago. The key realization about this, is that it is contrary to the notion that any burden is worth it if it saves demonstrable number of lives. In the extreme, the fatuous notion that "if it saves one life" is contradicted by the fact that 10,000 lives lost would result in a different level of response than would the prospect of 3 million. For some reason, 10,000 deaths may be accepted as part of the human condition, but one death cannot be accepted at all as a point of  public discourse.

At some point it has to be made clear whether decision-makers are continuing to make decisions based on models or whether they are doing so based on the three months worth of data available to them. It should be a matter of principled decision-making and competent governance to describe the criteria on which the decisions are based. can life begin to return to normal when the number of daily new cases declines to a pre-determined value, or percentage of the peak value? Is the consideration the number of daily deaths? Number of ventilators? Hospital capacity? Number of tests?

Data are collected for various purposes and those purposes affect how the data are collected and interpreted. There may be one purpose that prioritizes accuracy over inclusiveness, and therefore would reject death counts that included those that were never tested for coronavirus. Another interest may value inclusiveness over accuracy and be more accommodating of "presumed" cases. Some data such as lactate dehydrogenase values may be dismissed by physicians caring for patients as not likely to affect management, but these same data may be essential to constructing databases that provide more useful models of what factors determine disease severity and prognosis. Other data may be useful for risk stratification or resource allocation, or to justify reimbursement requests. In short, the value of data depends on the context and purpose for which it is collected. Data that is essential to some endeavors may be next to useless for others. IF the data we have available forms the basis of policy decisions, this fact must be considered. Are the data appropriate to policy under consideration, or are they skewed by other interests?

An analogous issue pertains to "experts." These people, who may be quite accomplished in a particular field, but who are not sympathetic to wider policy needs, may advocate for data that are relevant to their own fields and curiosities. Thus, data regarding the effectiveness of a particular intervention, such as convalescent plasma, may be useless if it is not collected in the context of patient randomization or placebo control, even though these factors may be irrelevant to family members who have a relative in tenuous condition on a ventilator.

Other policy decisions defy easy measurement regardless of the procedures by which data are collected.. It is unlikely that there will ever be a serious estimate of how many lives were saved, if any, by the distinction between essential and non-essential items that could be purchased from a store that sells both. Of course, it would be possible, and perhaps irresistible to construct a model that would provide an estimate, but when we get to that point we may as well begin meta-modeling and ask how much harm or benefit resulted from relying on models in the first place.

Coronavirus: Orphan issues

1. Occident and Orient. It is difficult not to notice the striking difference in coronavirus cases and deaths between places like New York and Italy on one hand, and Oregon, California and South Korea on the other. It is tempting to wonder whether there is some intrinsic difference in the virus that afflicts western Europe, and which may have then spread to the eastern United States, and the one in east Asia that may have then spread to the western United States.

2. Who dies. It is possible that we have reached the point in the spread of the virus, and the resulting suppression of everyday activities, where we are now trading off some deaths against others. It is possible perhaps that preventing the coronavirus-related death of an 80 year-old cancer patient will result in a fatal heart attack in a 68 year-old diabetic, because "routine" care that would have prevented such an outcome was foregone in the interest of "social distancing." The same may be pondered regarding the 85 year old Alzheimer's patient who persists three weeks on a ventilator, while another patient has a massive stroke because his endarterectomy for carotid artery disease was considered "elective." It is certainly possible, if there is a second wave of infection, that at least someone who would have gotten the infection the first time around, survived and developed immunity, would succumb of avoiding the infection the first go-round but acquiring it in the encore.

3. Decision and policy-making. It has been argued, by authors such as Malcolm Gladwell, if I recall correctly, that specialists have deeper knowledge but that generalists make better decisions. This is at least plausible, and if true suggests that the present approach of having political leaders, who are elected on political criteria, not leadership capacity or a history of wise decisions, deferring to the advice of narrowly credentialed experts is not optimal. Experts bring a blind-men-and-the-elephant narrowness to their opinions. They should not be expected to see the big picture, but then neither should the politicians. Experts have an interest in their fields, politicians have an interest in politics, but neither of these necessarily results in good policy. Throw in that the experts do not know nearly as much as they should, and the politicians have other interests that compete for consideration, and one would not expect policy to have nearly the beneficial effect on the epidemic as other factors.

4. What was necessary. The previous point naturally leads to another: what interventions that have been prescribed by various governments and organizations had the most effect on the spread of the virus, if any of them did? The experience of New York may well be considered a worst-case scenario. Whether it was virulence of a particular strain, the peculiarities of the public transportation system, population density, incompetent response, or likely a combination of multiple factors,  it is obvious that what worked elsewhere did not work in New York. From this we may conclude that certain interventions were ineffective, either because of environment, virulence, demographics or other factors, and that these ineffective interventions could have been foregone. So what worked elsewhere?; Was it necessary to "shelter in place" and shutter large parts of the economy? The experiences in Sweden, South Korea, and South Dakota suggest that, in certain environments, the answer is "no." The key factor is what interventions impede the most efficient means of spreading the virus. Given what we know, it seems at least plausible that the planet would have the same ball-park number of cases if the interventions were limited to: wearing masks, eating most everything with a clean utensil rather than hands, sanitizing hands after touching objects that the general public touches, such as door handles, light switches and plumbing fixtures.

5. Factors. It seems obvious that there is no one factor that accounts for the differences in COVID-19 experience between New York and Washington State. The difference is not due to smoking habits, ventilators, age, or the subway. There are likely multiple factors which formed a perfect storm around New York. The "lockdown" interventions may have had some positive effect, but more significant factors overcame them. There likely was no amount of mandated social distancing that was going to contain the spread of coronavirus in New York, and no intervention that was gong to keep the case fatality rate commensurate with South Korea or Germany.

6. Probabilities. It is helpful to think of the virus and the disease that it causes in terms of probabilities: each exposure has a certain probability of transmitting the virus, each case has a certain probability of being asymptomatic or minimally symptomatic. Each severe case has a certain probability of ending up on a ventilator, and a certain portion of those, of dying. The idea of interventions is to lower the undesirable probabilities. Wearing a mask likely has some modest effect on the probability of transmitting infection from an infected person to an uninfected one. Interventions such as remdesivir and hydroxychloroquine likely decrease the probability, without making it negligible, of proceeding to more severe disease or resulting in death. The goal of intervention is reasonably to lessen the probability of undesirable outcomes keeping other valid concerns, such as the economy in mind. At a certain point, more and more stringent restrictions hit the point of diminishing returns so that they induce harm more than mitigate risk.

7. Models. Models have not fared well in this crisis, for the simple reason that they have not provided accurate, or in some cases even reasonable predictions. This observation is not limited to epidemiologic models; it also applies to economic and even political ones. One flawed model is that expressed by Governor of New York that if severe restrictions "save one life" they are worth it. This is a hopelessly flawed model of the facts. There is no way of measuring either the cost or the benefit. If a person's life is "saved" until he tests negative for coronavirus, only to die of a ruptured brain aneurysm a month later, has a life been saved? What sacrifices were justified by this outcome? Furthermore, this reasoning does not translate to other concerns. It is difficult, for instance to apply the same reasoning to the distinction between "essential" and "non-essential" businesses. If a business is essential to just one person, say, the owner, is it essential, such that it is arbitrary to distinguish between hardware stores and hairdressers?

8. Assumptions. The news and social media are full of unjustified assumptions. One is that distinguishing between essential and non-essential provided anything more than a cosmetic benefit, beyond what what people could achieve themselves by observing reasonable behaviors to minimize the spread of the virus. The second, related one is that "emergency powers" and draconian restrictions were necessary or even helpful. A third is that a person who is infected with the virus is therefore immune, and that a vaccine is a foregone conclusion. None of these are beyond doubt. There is an argument to be made, but it is just an argument, that "flattening the curve" saved lives. No one knows. There is an assumption that some insight lurks in comparing the 2009 H1N1 epidemic with this one. The differences are significant, not the least of which is that H1N1 is from a class of viruses for which immunization has been shown to be an effective strategy.

Coronavirus: What if...?

In order for models to be useful, it is only necessary that they provide reasonably accurate predictions; it is not essential that they detail the exact mechanisms that underlie the things that they represent. It is very common for people to use anthropomorphic explanations for phenomena that do not involve characteristics or capabilities of humans, for example when we say say that an electron "sees" an electric field, or that nature "abhors" a vacuum. It is sufficient that that ascribed characteristics permit an inference as to how the system being modeled will behave.

Likewise, fiction writers can ascribe any manner of fantastic or even impossible mechanisms in order to make their stories work. This is essential to science fiction and ghost stories, and to any manner of heroic epics. The mechanisms themselves do not have to be reasonable or real, they just have to make the story work.

We may take a similar approach in contemplating the coronavirus. One of the most striking facts about our developing experience with the virus is the wildly varying effects that it has on different places and different populations, and the seemingly contradictory and inexplicable observations that arise from that experience. We note, for example the rather severe course of contagion in New York, and Italy, and compare these with rather mild experiences in Poland or Oregon. We are struck by the marked difference in mortality between Italy and Germany. We note the oscillating pattern contained in the daily new case charts from various places. We might ask ourselves, if we were novelists, trying to craft a story that contained these phenomena, what mechanism would we choose? Alternatively if we were to try and derive a model, with the priority of making appropriate predictions, what sorts of behavior would we assume for the virus and the populations and environments in which it circulates?

We might start by ascribing strategies, both to the virus and to the human population that it affects. We need not create a cognitive, planning agent. that manages such strategies, but simply accept that the behavior of the virus and its interactions with humans proceeds as though there were such an agent. One mechanism that we might contemplate, for example if we were writing fiction about the virus is epigenetics; the idea that organisms change as a result of differences in gene expression rather than in the genetic code itself. We have two possibilities here: that the organism subject to epigenetic phenomena is the human population subject to infection, or the virus that does the infecting. We might also consider that it could be both.

This gives us a starting point, either for a story or of a model that epigenetics represents a mechanism by which organisms appear to pursue strategies that optimize some outcome of benefit to the organism. For example, it may appear that the strategy of contagion of the virus requires that not all infected people die. Therefore the virus may behave as though there were some feedback that affects expression of viral genes that slows spread when large numbers of people are infected all at once. This may explain (certainly not the only explanation, and by no means an exclusive or even correct one) the appearance of the rhythmic peak-and-trough pattern observed in the documented experience of widely separated countries and states. It is possible to at least conceive that there is an epigentic phenomenon by which pathogens are regulated so as not to kill off the entire population of hosts subject to infection.

Another possibility is that there is an epigenetic phenomenon in people, such that innate immune responses, for example limit disease spread in patient who are not infected and therefore have no specific immunity to the disease. This may explain the experience of the Diamond Princess in which only about a fifth of the passengers were infected while on board, but some became infected after disembarking. It may also explain why some places like California and in particular homeless populations are not awash in dead bodies, even though the size of the antibody positive population seems rather modest. One of the interesting observations made by Daniel DeFoe in his journalistic-fiction work A Journal of the Plague Year is that the severity of disease in those infected declined as the contagion waned. Even though the book itself was fiction (DeFoe was only 6 at the time of the Great Plague) it was based on journals and recollections of family members, and therefore may reflect an actual phenomenon. If so, it would be consistent with an epigenitic basis for contagion and virulence.

This same phenomenon (again a literary device or modeling convenience, not necessarily a biological fact) would explain the wide variety of disease severity, the appearance of asymptomatic carriers and most significantly, the low absolute prevalence of coronavirus infection. The same approach can be used to account for the widely divergent rates of mortality observed for the virus. It may be assumed that the concept of "strategy" as mentioned above is merely an anthropomorphic device that provides a point of reference for why things may behave as they do. It implies no conscience and surely no empathy or sentimentality. We note that when bird flu emerged, the rational response was to slaughter millions of chickens. Killing off the host significantly impedes spread of the virus. It may be reasonable to consider an epigentic strategy in human populations as well: kill off those most likely to spread the infection to others, without commensurate detriment to reproduction or survival of the larger group. Furthermore, we can contemplate an environmental influence on these mechanisms. Italy has a higher mortality than Germany, and New York has a higher mortality than Oregon because they are different environments. They people in them may not seem outwardly different, but the way in which individual physiology interacts with the environment is different.

An obvious objection to even considering an epigentic, or other mechanism that requires some manner of organism level communication, effect is that it defies explanation. It seems fantastic to consider that virions may alter genetic expression, or that the immune response of unifected humans can depend on the infection status of those around them. There are however precedents for observing changes in population dynamics and disease transmission that seem to reflect a strategic element hard-wired into biology. It is useful to think of the virus, the human population, and the environment as components of a system, and a system which contains complex feedbacks and dynamics. Complex systems operate about points of equilibrium, and these points are determined by the dynamics. One interesting article that touches on the point is helpfully titled Ecological Feedbacks Can Reduce Population Efficacy of Wildlife Fertility Control. This is an article by Ransom, Powers, et al., in the February 2014 issue of the Journal of Applied Ecology. It contains the observation that "Disease transmission was 28% higher in populations of possums Trichosurus vulpecula with sterile females, illustrating the potential for decreased survival in fertility-controlled populations." The interesting thing about this statement is that is suggests that there is some feedback by which the presence of sterile females in an animal population affects transmission of disease; it suggests that there is some mechanism by which the fertility of some female members of a population feeds back, i,e, is communicated to other members of the population and affects disease transmission.

This is not to argue for an epigenetic mechanism driving or controlling a pandemic. It is merely a speculation that illustrates that if we want to explain the variety of observations and data, conflicting and varied experiences, the relatively benign and severe experiences in places where one would expect similarity, etc., our understanding of what affects the spread of the virus and the nature of the disease that it causes must necessarily be much more advanced than it currently is.

Coronavirus: Patterns

Here is a histogram of the daily new coronavirus cases in Sweden:

Note the peaks indicated by the vertical marks. Also note the regularity. Here is a similar plot from Germany:

And Italy:

And from Michigan, although in this case the plot is of new cases by date of onset:

Each of these demonstrates a regular exacerbation/remission pattern in the reporting of new cases. There are two possibilities associated with this observation: Either it reflects an underlying phenomenon or it does not. It is certainly possible that what is illustrated above is a coincidence, or perhaps some quirk in the way tests are collected, run and reported. The apparent pattern may simply be apophenia, the perception of patterns where there are none, or it may be a pattern reflecting something other than the way the virus infects people. 

The other possibility is that the patterns above reflect a characteristic of viral spread in populations. It appears as though there is an oscillation in new cases superimposed on the underlying bell-shaped curve. If this is the case, what might account for it? As proposed previously, this may reflect the possibility that the spread of the virus is more complex than simply the accident of a person encountering an inoculum of virions and becoming infected, and then passing it on to others. The dynamics of virus spread seem to involve other, not yet explained factors. Even though there is no plausible feedback mechanism currently being considered to understand how the contagion grows, peaks and recedes, inspection of the charts above indicates that, in certain cases at least, the virus behaves as though such mechanisms are present.

Coronavirus: Decision-making

One of the more erratic aspects of the current contagion is the approach to decision making with regard to controlling the spread of the virus, treating those infected with it and minimizing the associated adverse consequences. These decisions are hampered, as has been mentioned in previous posts, by a frenetic approach to managing data regarding the epidemic, as well as to the large amount of uncertainty and knowledge deficits that afflict even the most esteemed of those experts whose opinions affect those decisions. These factors are exacerbated by variances in the motives of decision-makers, as economic, political, scientific, humanitarian, and practical considerations compete for consideration in decisions-making processes.

Because of the lack of detailed knowledge of the SARS cov-2 virus, decision-makers defer to experts who, subject to the same disabilities, must rely on surrogates and educated guesses. As a result, we practice social distancing policies derived from conjecture and old habits. The six-foot rule, which is a staple of social distancing dogma derives from nearly 90 year old investigations into the spread of certain viruses by coughing and sneezing. Our six-foot rule is a decision based on legacy habits because we don't have anything better, Similarly, the 14 day quarantine rule is based on observations of members of the coronavirus family that are most definitely not SARS cov-2. The estimates of death and extent of infection are based on theoretical computer models that are so dependent on unsupported assumption, that the estimates themselves may as well be assumptions. Rather than assuming the inputs into models of questionable reliability, we could as easily assume the outputs.

It is not unreasonable for for experts to rely on conjecture, analogies, surrogate experiences and educated guesses in the absence of more reliable and rigorous data and more detailed understanding of the processes. It is unreasonable to pretend that these models, predictions, guesses and theories are accurate simply because they are the best we have. It is unreasonable to pretend, in other words, that guesses and conjecture are accurate simply because an expert with inadequate information and understanding adopts them.

Some hospitals have adopted guidelines for the use of hydroxycholoroquine and azithromycin in COVID-19 patients. These often require the patient to exhibit a declining course and to be at high risk of needing intubation and mechanical ventilation. Other physicians question the reasonableness of this, arguing that earlier intervention with these interventions might prevent the deterioration that occasions consideration of second and third line interventions. The decision making here is again reasonable, but certainly not unassailable. The assumptions are that hydroxycholoroqine and azithromycin are unproven interventions, which is undoubtedly true, and therefore both the benefits and risks are uncertain. If however, the patient is at greater risk of death, in the absence of proven interventions, the risk benefit ratio shifts in the direction of intervention. This reasoning does not make either providing the therapy or withholding it correct. It merely illustrates that the model of decision-making, in this example risk-benefit analysis in the face of uncertainty results in a class of decision that might be different under different decision-making criteria. A similar principle is seen in the reluctance of certain medical advisors to resist prescribing these medicines because there is no conclusive proof of their efficacy. This position is wholly defensible within a particular context, i.e. protecting the science and evidence-based foundations of modern medicine. It is less defensible in the context of treating patients infected with a novel pathogen for which no proven therapies exist.

Other decisions demonstrate the same criteria based sensitivity that may make them seem irrational. One example is the prohibition on purchase of "non-essential" items from stores that also sell essential ones. One can contemplate that allowing purchase of non-essential items might lure people from their shelters when they otherwise would remain at home. This, however is a third-order consideration. It is extremely unlikely that the ban on purchasing child safety seats would save a single life that would otherwise be lost to COVID-19. It is not an example of reasonable decision-making but rather an irrational, panicked excess by people who do not seem particularly well suited to such decisions. 

A similar principle is observed in the odd orders by certain governors to prohibit practitioners from prescribing choloroquine or hydroxycholoroquine to patients diagnosed with COVID-19. Again there is a certain cursory rationale that may be invoked regarding hoarding or capricious use. However, none of these considerations even remotely abrogates that principle that therapeutic decision should be made between a physician and the patient in the best interest of the patient. Certainly, it might be reasonable for a state medical board to warn that prescribing practices other than to treat active infections would be considered unprofessional conduct, and leave it to the medical profession to regulate, well the practice of medicine. For politicians to insert themselves into the physician-patient relationship is one set of decisions that is unlikely to age well.

Decisions regarding medical and public health interventions are confounded by incomplete, shoddy and manipulated data. They are affected by sometimes conflicting priorities, such as maintaining the evidence based fundamentals of medical care, and the urgencies of a particular case. They are hampered by considerations of political expediency, economic interest and the burdens placed on everyday life, with no tangible evidence of benefit. They are obscured by uncertainty regarding goals: are we trying to flatten the curve, minimize infections, achieve herd immunity, or something else? They are impaired by reluctance to answer hard but inescapable questions: how many deaths or hospitalizations are "worth it" to start getting back to normal? Serious people know that the reasonable answer is some number other than zero, but are reluctant to say so because other considerations are the basis for that reluctance.

One thing that this experience with the Wuhan coronavirus has demonstrated is that, quite frequently, the people who are in a position to make important decisions are not in those positions because of a demonstrated ability to make good decisions.

Coronavirus: Does social distancing work?

When researchers want to determine if a new therapy has a beneficial clinical effect, they conduct a randomized trial. They divide the population to be studied into different groups, some of whom will receive the treatment being evaluated and others who will not. The outcomes in the different groups are then studies to see if the therapy had any significant effects, both beneficial and detrimental. The purpose of randomization is to try and make the different groups similar to each other, so that, for example the average age or proportion of women is more or less equal. The idea is to apply different treatments (the one of interest, and either placebo or some other intervention) to more or less similar populations to allow observation of the effects of the intervention.

Conceivably, one might also observe differences if the same intervention were to be applied to groups having different characteristics. In this case, however, it is much more difficult to determine if the intervention does anything, because differences between the groups might account completely for differences in outcome. There is however, one observation that can be made: whether the intervention works for all groups regardless of differences between them. This is the situation we have with the social distancing and stay at home orders currently affecting the majority of the United States. While we cannot say for certain that social distancing does or does not work, we can say that it does not work the same everywhere. The experiences of New York and California discredit the idea that the spread and effects of the Wuhan coronavirus are simply matters of a nasty virus and avoiding non-essential travel.

It is not possible for anyone to say that earlier social restrictions or government intervention would have contained the spread of the spread of the virus, or that the death count would have been higher had not such efforts been imposed, nor is it possible to say they had no benefit. There is simply no way to know. It seems reasonable that the less interaction people have with each other, the less likely an infected person is to spread the infection during the interval in which that person is contagious. Thus, social distancing is reasonable. But, as is possibly the case with hydroxychloroquine, social distancing and isolation are only discrete factors among many that contribute to the profile of disease spread. They may influence some aspect, such as rate of spread, and thus impede, but not control the virus. The experience in New York suggests that either social distancing has only second order effects, or that the environment of New York makes social distancing efforts either less effective or less practical.

What the disparate results of social distancing policies suggests is that the spread of the virus depends on conditions, that is , the environment in which it spreads, of which social distancing is only one factor. The spread of the virus is likely governed by processes of which we, including our most esteemed experts, are unaware. The virus interacts with the environment as a constituent of a system, likely involving complex interactions, and un-accounted-for processes. It is obvious that viruses have no cognition, that they devise no strategies nor coordinate no actions. The same is true of water molecules, yet snowflakes form with symmetry and remarkable consistency in many of their characteristics, responding only to the conditions in which they form, and the inherent characteristics of water. Epidemics may behave the same way. Just as conditions determine the ultimate shape of snowflakes, they determine how fast and how far coronavirus spreads, and how many people are asymptomatic and how many people die.

What our experience tells us to date is that social distancing and isolation are reasonable, but also that we have no real idea of how effective they are.

Coronavirus: Therapy

The discussion of hydroxychloroquine and remdesivir as treatments for conronavirus infection understandably attract a lot of attention. Certainly, there will be extensive efforts to find interventions that shorten the duration of COVID and limit the severity of the disease. It is too early to tell if any reasonable therapeutic agents are on the near horizon, but some general observations can be made regarding the issue.

I. Vaccine. It certainly seems reasonable that a vaccine will be developed to mitigate the spread of coronavirus infection. It is not reasonable to assume that this is a foregone conclusion. Depending on the year, influenza vaccines have only limited efficacy. Some viruses for which vaccines are sought do not have them. While it is expected a vaccine would provide immunity, as for smallpox or measles, there is no guarantee that this will be the case for SARS Cov-2. It is not clear if people who displayed symptoms of COVID-19 have developed immunity, or if only some of them do. It is not known if a widely available vaccine would still leave large "vulnerable" populations, such that the social distancing practices currently in use would not still be required if a vaccine were available.

II. Choloroquine and hydroxychloroquine. The evidence of efficacy of these agents seems to a little more substantial than merely isolated anecdotes. This is particularly true of reports of efficacy against SARS Cov-1. There are plausible mechanisms, or perhaps constellations of mechanism by which to conclude that efficacy is at least plausible, but even if it were scientifically established that these medicines have a therapeutic benefit, we would not expect them to function as "cures." A reasonable way to look at choloroquine and hydroxychloroquine is that they improve the chances of resolution of symptoms without life-threatening crises. They improve odds; they will have more benefit for some people than others. One would expect that different study designs will reflect this fact in that some studies will show a discernible benefit while others will not. This will not mean that the drugs have no effect, but rather that the effects are not uniform and are contingent upon factors that may not seem obvious when the studies are designed.

III. Convalescent plasma, IL-6 inhibitors and monoclonal antibodies. These interventions are primarily intended for extremely ill individuals at high risk of death; i.e. those that have severe lung disease. Here we may contemplate a relevant possibility: that the risk factors for developing COVID-19 once infected with coronavirus are different than those associated with developing a life-threatening case. One way to look at this is that COVID-19 with viral pneumonia is a different disease than COVID-19 without viral pneumonia. This is true even though the causative organism is the same in both cases. It is the same type of distinction made between pneumonic and bubonic plague, or between ordinary, modified and malignant smallpox. The reason for making the distinction with regard to coronavirus is that therapy is likely to differ between the different disease manifestations. For example, early in the course of disease, fever may be beneficial, but may then become damaging to lung tissue once ARDS (acute respiratory distress syndrome) has developed. Immune modifying agents may be harmful if given early, and beneficial once mechanical ventilation is required. It should be expected that the course of disease is affected by multiple factors, some of which may not even have been guessed at, much less studied and understood.

IV. General principles. Returning to chloroquine and hydroxychloroquine for a moment, we may observe that many useful pharmacologic agents fall into two broad categories: blockers of one form or another, and enzyme inhibitors. Beta blockers and calcium channel blockers are obviously members of the former class while statin drugs, NSAIDs, and a great many antibiotics are examples of the latter. What these have in common is that they interfere with the metabolic pathways associated with biological processes, both physiologic and pathologic. The experience with choloroquine and hydroxycholoroquine is that they affect a large number of metabolic pathways, affecting for example the metabolism of heme, the regulation of inflammation and Toll-like receptors, as well as the acid-base balance within cells. It is certainly possible that some of these effects influence the course of infection in humans, through as yet unknown mechanisms. It is also useful to note that the beneficial effects of quinine, from which chloroquine and hydroxychloroquine are derived were discovered by happenstance, (the same with biguanides, penicillin, and nitrogen mustards for treatment of cancer) not rigorous or rational design and development. It may well be that they preferred management for COVID-19 is discovered the same way.

Coronavirus: More thoughts

1. Discrete observations about this virus do not extrapolate well. This was mentioned in the previous post titled "Coronavirus: the uniformity error." If, for example, we tried to extrapolate the experience of California at this moment to the rest of the United States, we would expect to have 192,440 total cases and 5440 deaths. Instead, we note that, while California has 566 cases per million people, New York has 9,233. Texas has 474, Nevada 924, Oklahoma 477 and West Virginia 323.

2. What the above suggests is that the spread of the coronavirus is determined to a great extent how the virus interacts with the environment, beyond simple considerations of population density and mitigation procedures. Social distancing that works in Oklahoma apparently does not do so well in New York or New Jersey. The reason for this is likely to involve many factors: weather, umber of people who live in multi-family dwellings, use of public transportation, hygiene habits, etc. What can be said with some confidence is that run-of-the-mill social distancing precautions that work elsewhere do not have as much effect on high-probability exposures in New York and New Jersey. Another way to look at this is that New York and New Jersey are much more favorable environments for spread of the virus.

3. The caveat about extrapolating applies to isolated observations as well. There appears to be much heed paid to a report from a phlebotomy technician in Illinois that 30%-50% of people tested are positive for SARS-cov2 antibodies, or that 15% of a German village also demonstrate positive antibodies. This is in contrast with San Miguel county in Colorado (which intends to test the entire population there) where less than 1% are anti-body positive.

4. Most places have hit the point of diminishing returns regarding additional social distancing orders. Now such orders are likely do as much harm as good.

5. The risk factors for catching the virus are different than the risk factors for dying from it.

6. Since the French study upon which much of the confidence in hydroxychloroquine is based reported decreased viral shedding as its endpoint, it is reasonable to at least ask if that medicine interferes with the viral testing, and whether this might lead to people being declared cleared when they are in fact still contagious.

7. The incidence of diagnosed cases is still very low, and the mortality in certain places is still very high. Again there is likely an environmental component that has escaped our notice, as well as genetic and cultural factors that we are conditioned to not notice.

8. The rise of coronazis, people who seek to enforce social distancing recommendations beyond all reason, is one of the more depressing non-medical aspects of this epidemic. Common sense tells us what are the most likely behaviors to spread the virus; a battalion of emboldened Gladys Cravitzes is unlikely to provide additional benefit.

Coronavirus: Social distancing

Do increasingly draconian social distancing measures accomplish anything? Here is one way to look at it.

Let us assume that there is a particular type of exposure, say using a public restroom, and that this is associated with an average probability, p₁ of becoming infected. The probability of not being infected by this exposure is 1-p₁. Assuming that a person's risk of becoming infected with repeated exposures are independent of each other, the probability of not being infected in two exposures is (1-p₁)², and the resulting risk of being infected is 1 minus the probability of not being infected or

P_I=1-(1-p₁)²

For N₁ such exposures, the risk of being infected is

P_I=1-(1-p₁)^N₁

The same reasoning holds true for different types of exposures with different probabilities of transmitting the virus.

For two such exposures the probability of becoming infected is

P_I=1-(1-p₁)^N₁(1-p₂)^N₂

where p₁ is the probability of infection associated with the first exposure, N₁ is the number of the first type of exposures, p₂ is the probability associated with the second type of exposure and N₂ is the number of such exposures.

We can extend this to any number of exposure types. The key point is that different exposure types are associated with different probabilities of transmitting infections. The effectiveness of social distancing depends on its effects in minimizing the Ns associated with the various exposure types. There is much more benefit to decreasing the number of exposures associated with a high risk of transmitting the virus, and less so to those with very low probabilities unless the baseline N of such exposures is extremely high.

The high probability, and thus risk, exposures are those associated with behaviors that have a high risk of inoculating the nasopharynx or oropharynx, such as sharing a drinking glass, or eating something with unwashed hands after touching a contaminated surface. Low risk exposures would be taking a walk in a park. Mid-level exposures would be shopping in a grocery store.

Avoidance of high risk exposures, for the most part do not require official enforcement. Given adequate information, most people would do an effective job of minimizing risk. The more draconian, and often stupid prohibitions, result in diminishing returns, e.g. buying "non-essential items" when also buying essential ones, because they affect very low risk exposures that have minimal effect on the overall risk.

There is no question that there is a benefit to social distancing. However, the heavy lifting is done by common sense, not politicians and bureaucrats with a need to look like they are doing something.

Coronavirus: A few thoughts

A few passing thoughts on the current state of following the coronavirus epidemic:

1. Apples and oranges: As mentioned yesterday, changing the criteria for determining who is infected with corona virus, who has recovered, and who dies of the disease makes it very difficult if not impossible for anyone, including "experts" to track the course of the contagion. It is difficult to make week-to week comparisons of reported data when those data measure different things in different ways.

2. There is a noticeable tendency for people to seek single-cause explanations for differences in the coronavirus experiences of different locations and at different times. Some examples include: the extent of testing; the presence and timing of social distancing, if any; the age of the population; the extent of smoking and other habits; the nature of financing of particular healthcare systems, etc. It is unlikely that there is any universal intervention or cause to explain difference observed across populations or from time to time. The experience of South Korea is unlikely to translate to New York, or Spain, or anywhere else. Differences in the effects of coronavirus, its spread and mortality are much more likely due to constellations of factors that interact in unknown ways and which are not always amenable to observation or measurement. The single factor idea is a fallacy.

3. Similar to the above, there are a great many isolated observations that should be considered as representative phenomena only with great skepticism. Such observations include "young people are dying of the virus," "people who were thought to have recovered are testing positive again," and alleged cures associated with various interventions. These are anecdotes and, to the extent that they are useful, are such because they remind us that generalities associated with this virus come with a whole lot of asterisks. One should be very cautious about generalizing the experiences of one group of people to wider populations, even if the isolated observation is itself true.

4. The observation above is highlighted by the fact that data are all over the place. Out of 7.7 billion people on the planet there is not a single one who legitimately knows the prevalence of the disease, the mortality, whether the infection confers immunity, whether abnormally low or abnormally high rates of infection or death are due to such things as government responses, or people's natural behavioral changes to an acknowledged threat. Because the data are all over the place, it is almost impossible to assess the effect of interventions. A person looking at the experience of New York and comparing it with say Oklahoma or Wyoming, might be tempted to say that social distancing does not work. (Although a more pragmatic approach is to consider that the differences between New York and elsewhere is due to unique combination of factors, rather than one or two things). It is not only the reported data, which is contaminated by constantly changing criteria, that is all over the place; so are the predictions of various models and experts and credentialed sooth-sayers. This will eventually reveal itself in the public becoming distrustful of those who purport to be managing this crisis. There is only so much "3 million deaths... no 600,000, no, 20,000, no, 125,000, no 400,000...,""we don't have enough ventilators, we have enough ventilators, we have too many AND not enough...","go out and live your life, no, stay home, only go out for necessities,...hey, those aren't necessities..." etc. before people start suspecting not only a lack of reliable data, but of competence and good faith.

5. New York is an outlier, no matter how you look at it. On the one hand the infection and mortality rates are noticeably higher than one would expect from the country as a whole. Yet supposedly a large number of people are dying of coronavirus at home without a formal diagnosis, and the percentage of positive test results is higher than elsewhere. This would suggest that the already elevated reported percentage of the population infected underestimates the true number of infections. Again, this is most likely accounted for by a constellation of factors unique to New York, but still, the anomaly is quite noticeable, and suggests that the social distancing strategies that seem (whether this is true or not we don't know) to be beneficial elsewhere are of markedly diminished efficacy in New York.

6. No one can say with certainty whether there will ever be an effective vaccine.

7. Many of the countries, and American states who are assumed to report reasonably accurate data demonstrate an interesting phenomenon. The daily new case profiles seem to contain oscillations, with a period of six or seven days when there seem to be more, then less new cases, and these are superimposed on the underlying bell-shaped trend.

8. Using the data from Colorado, which reports new cases both as to date of onset of symptoms and date of diagnosis, it appears that "infectious period" used in the simple spread sheet models described previously is nine days.

Coronavirus: Data

There is probably more about the coronavirus that we do not know than that which we do. Our knowledge is constrained by available evidence , which consists primarily of reports of daily new cases, deaths and total number infected. No reasonable person expects that any of these data are accurate in themselves. There are too many sources of uncertainty, too many variables that affect the ability to characterize the extent of the contagion with precision at any point. The best we can do is to assume that the general trends and tendencies of the data that are reported reflect similar trends and tendencies in the wider world. This is also challenging.

The data are affected not only by changes in the course of infection, but by constant changes in the availability and use of testing, of suspected manipulation and misreporting of data for non-epidemiologic ends, of changes in procedures for attributing particular symptoms or deaths to coronavirus without detailed investigation, and the lack of standardization from place to place or from time to time within the same place.

A paradox arises because we rely on models to provide surrogate data for the things we cannot readily observe, but these models depend on the data that are available, and these are of questionable consistency. As a consequence, the models upon which we rely for planning and policy are likewise of questionable consistency.

A main source of uncertainty is attributing symptoms or deaths to coronavirus in the absence of testing. We can note that there was a dramatic increase in the number of reported cases in China on February 12, 2020 when the criteria for diagnosis changed from a laboratory verified standard to a "clinical" one. We would expect that such a procedure would result in an increase in the number of reported cases, and also that such number would include people who are not in fact infected with coronavirus. This does not improve our knowledge of the state of the contagion, because other sources of uncertainty, such as people who are neither tested for the virus, nor symptomatic may nonetheless have it. Changing the criteria has the primary effect of increasing the uncertainty, rather than increasing the accuracy of assessment.

A similar principle applies in the matter of attributing deaths to the virus. Doing so without a laboratory-confirmed diagnosis, and instead allowing "suspected" cases to be counted is likely to overestimate the true number of coronavirus-related deaths. Changing the criteria creates uncertainty, and we are likely much better off with a system that may result in an inaccurate count, but reliable profile of the trends and volatility of observed cases. Changing the criteria upon which deaths are attributed to coronavirus taints both the absolute numbers associated with the data as well as the inferences that may be drawn from them.

Attributing deaths to coronavirus in the setting of pre-existing conditions is inherently subjective. This is especially so in cases attended by significant pre-infection debility and frailty. It would be helpful, though not practical to attribute deaths to coronavirus only if the life expectancy of the person was at least a year in the virus. It used to be a principle of criminal law that an injury inflicted by a defendant was not a cause of death if the victim survived the assault by more than one year. The ability to assign causation is always fraught with sources of error, and uncertainty, and the point of changing the criteria for doing such in the middle of a pandemic would seem to serve little purpose. This, again assumes that the true information of interest are the pattern and trends observable from the data reflect the course of the spread, even if the absolute values of the either over-estimate or underestimate the true circumstance.

These uncertainties are obvious in the constant state of dispute regarding the mortality of the virus, or the number of asymptomatic carriers, or the R₀. These uncertainties are exacerbated by misguided changes in assessment and attribution criteria. The errors associated with accepting subjective determinations of infection are illustrated by the data published by the Colorado Department of Health. These data reveal that, of all tests administered, no more than 20% are positive. It should be assumed that people are tested because they have symptoms consistent with the infection, or are at an elevated risk of contracting it. We may assume that of those tested based on symptoms, a certain number would have been diagnosed with coronavirus under the "clinical" criteria adopted in China, and thus the number of cases would be falsely increased. Countering this, a number of actually infected patients, symptomatic or not would not be tested, either for logistic reasons or reasons personal to the person affected. These would result in under-assessment of the true circumstance.

The upshot of this all of this, is that it is more important to have a consistent method of diagnosing cases and attributing deaths, both geographically and over time, than it is to constantly be tweaking criteria in an ultimately pointless attempt to make sure all cases are counted. At a certain point the experts will be tempted to alter the criteria of measurement to conform to models, rather than interpreting the data as it is to improve those models.

Coronavirus: Interim summary

To summarize the thoughts contained in the last several posts:

1. Points of equilibrium. The spread of the virus proceeds, in a given environment to points of equilibrium. These are points at which the number of new cases is balanced against the number of infected people who are no longer capable of passing the virus to someone else.

2. Conditions. There are only two conditions that need to be satisfied in order for the points-of-equilibrium model to be valid: resistance to spread of the virus must increase as the virus spreads, and the rate at which infectious people drop out is proportional to the total number of active cases.

3. Interventions. The points of equilibrium, and thus the numbers infected and infection rates can be altered by interventions. Whatever interventions exist in a particular environment at a particular time determine the point of equilibrium.

4. When interventions change, new points of equilibrium are established. The number of new cases will increase or decrease to accommodate the new equilibrium point. The default equilibrium point is not the point of herd immunity or the condition where everyone is eventually infected.

5. There are two competing hypotheses: that interventions affect the ultimate number of people of infected, and that they do not. If the former case is true, the goal of interventions is to limit the total number of people infected, if the latter is true, the goal is to control the rate of spread, with the idea of limiting deaths occasioned by inadequate healthcare resources.

6. The point of equilibrium model is consistent with both hypotheses.

7. Hydroxychloroquine is rational therapy that is not strictly a "cure" but has a reasonable mechanism to limit disease severity in infected persons.

8. Loosening mitigation efforts will result in an increase in case rate as a new equilibrium is reached, and this will happen regardless of when such actions are taken.

9. The actual peak of the epidemic occurs several days, roughly equal to the incubation period, before the observed peak.

Coronavirus: Opening up the economy again.

The effect of the Wuhan coronavirus epidemic is obvious. It is accepted that at some point the economy will have to resume, and that it is unreasonable, and frankly stupid to suggest, that the condition for doing so is that the daily number of new cases be zero. There is however understandable official reluctance to proceed with the loosening of social distancing practices that resuming economic activity necessarily entails. There are a couple of reasons for this.

One, there is a virtue auction going on. No politician wants to be seen as saying the number of old folks dying is "acceptable," that is, low enough to justify resuming economic activity. The auction occurs when politician A declares that the number of deaths, while tragic, regrettable, etc., is such that it is reasonable to loosen things up, politician B bids a lower number of deaths, to show that he cares more. It is a little like the meetings in the Soviet Union where politicians were unwilling to be the first to stop applauding the introduction of Stalin. Politicians do not want to be the first to say that some non-zero number of deaths is an acceptable trade off for letting people get on with their lives. This goes on until the people themselves decide that economic concerns predominate and pressure political leaders to change focus.

A second issue is that there is a fair amount of uncertainty as to what will happen regarding spread of infection if restrictions are relaxed in deference to economic concerns. The whole concept of "flattening the curve" seems to adopt a notion that nearly everyone will eventually get infected, and the idea is simply to control the rate at which that occurs. Dr. Fauci seems to subscribe to this view, and it relies on an assumption that everyone has more or less the same susceptibility to the disease. It includes that assumption that any loosening of restrictions and social distancing will result in uncontrolled spread of infection. This view however is more consistent with risk aversion and worst case scenarios than with actual experience.

Another model assumes that if restriction are held in place, the total number of cases will be less when the epidemic has ended. A third model, that discussed in these posts suggests that when restrictions are loosened, the will be an uptick in the spread of the virus, but this will be limited, as a new point of equilibrium is reached.

Each of these models has implications on a fundamental question: do the restrictions intended to control spread of the virus do any good?

The first model assumes that everyone will eventually get infected, but that the number of deaths will be limited somewhat because the rate of spread will permit the provision of medical services to people who might otherwise die without them. To determine if this makes sense, it is necessary to know how many people who receive medical care die anyway. How many people who survive mechanical ventilation would not have been placed on a ventilator if the spread of the virus were less constrained? What was the pre-virus life expectancy of these people?

The second model limits the absolute number of cases and consequently the resulting number of deaths. This implicitly rejects the notion that everyone will get infected. It also necessarily contemplates some mechanism by which the virus disappears. The difficulty with this model is that amount by which the ultimate number of cases is reduced is unknown, and also unknowable. The same considerations that apply to the first model also apply to this one. The reality is that it is unreasonable to freeze all activity except waiting for the number of new daily cases to drop to zero. Adopting this model may result in fewer deaths, it may not.

The third model, the one that considers that the rate of spread is limited because of two readily observable conditions, decrease in the rate of infection over time and previously infected people becoming no longer capable of spreading the infection, suggests that when disease mitigation efforts are relaxed, the rates of infection will increase to a new equilibrium point then stabilize. It suggests that not everyone will become infected. It does allow that the rate of spread can be controlled to some degree, as the mitigation efforts determine a particular point of equilibrium, which changes when the mitigation efforts change. This model thus supports a brief period of mitigation efforts, to avoid overwhelming the medical system, predicts a modest uptick in disease activity as a new equilibrium is reached, but also highlights the diminishing returns of prolonging mitigation efforts.

Given this, and assuming that the third model is the most predictive (an assumption based on observation, not rigorous scientific proof), a reasonable way to open up the economy would be, proceeding at the state level, in three day increments:

1. Make mitigation efforts, including masks and travel restrictions voluntary, but highly recommended.
2. Allow low risk enterprises, specifically landscaping, roofing, construction, hair salons, and infrastructure work to resume.
3.Remove restrictions on "non-essential" business, again highly recommending people adhere to prudent infection control practices.
4. Allow restaurants and bars to re-open with modifications such as hand sanitizer and wipes at each table, use of disposable menus, hand santizer outside of the restrooms, use of disposable pre-wrapped utensils, etc.
5. Allow all businesses except nursing homes, skilled nursing facilities and rehab hospitals to resume operations. Health departments should use local patterns of infection to determine when restrictions in these types of facilities, i.e. visitors, use of N95 masks and so on, can be relaxed.

The criteria for when to begin doing this should be when the average number of daily new cases is some fraction of the peak number of new cases, say 40%.

Schools should be allowed to re-open according to a more stringent criteria, say when the ration of new to peak cases is 25%.

Coronavirus: Hypothesis expanded.

The previous post noted the error that results from assuming uniformity in the way the virus spreads, who it affects, and what interventions are effective. There ore scraps of evidence and anecdotes that can be used to support diametrically opposed arguments. The current assumptions that underlie response to the coronavirus appear to based on the following assumptions:

1. The virus is highly contagious;
2. Everyone who has not already been infected has the same risk of contracting the infection in the absence of mitigation procedures;
3. Testing is somehow therapeutic, in that it allows for more targeted isolation practices and interventions;
4. Isolated observations are representative of universal facts.

This last one is responsible for vacillations such as wearing masks is pointless, wearing masks is potentially helpful, wearing masks is mandatory.

The assumptions noted above are worst-case defaults. They almost certainly do not reflect, nor explain the observed facts. An alternative hypothesis was suggested earlier based on a couple of assumptions that seem to be valid throughout a wide swath of nature. These are:

1. All natural phenomena operate about points of equilibrium, and when disturbed, seek new pints of equilibrium.

2. Equilibrium states are functions of environments; they are determined by how a particular phenomenon, such as spread of a virus, interacts with the immediate environment.

This post expands on thoughts previously discussed here
 https://z9z99.blogspot.com/2020/03/coronavirus-couple-of-thoughts-on-model.html
and here
https://z9z99.blogspot.com/2020/03/coronavirus-iv-hypothesis-as-to-what.html

The relatively low absolute rate of infection observed in almost all populations reflects a scenario in which the points of equilibrium exist at correspondingly low percentage of the population, typically less than 1%. This does not mean that the infection stops when 1% of a population is infected; it means that the rate of spread slows, naturally such that the number of active cases (deaths minus resolved cases) is relatively constant.

Point 2 above is instructive for purposes of mitigation efforts, and economic decisions and so forth. The equilibrium point is a function of the environment and the environment in turn is affected by mitigation efforts. If mitigation efforts are relaxed, the virus will not rage uncontrolled, it will seek a new point of equilibrium until some other environmental factor (such as vaccination, weather effects of viral survivability, etc.) changes it again. The reason that the experiences in New York state are different than the experiences in Washington state and that the experience of Sweden is different than that in South Korea, is that each of these is a different environment, with the virus tending to spread according to a locally-determined point of equilibrium. The environmental factors include genetic make-up of the population, cultural habits, mitigation efforts, crowding, transportation infrastructures, etc. The idea of an equilibrium point helps explain the relatively constant number of new daily cases in South Korea.

If the discussion of equilibrium points seems a bit hand-wavy, consider an extreme example. Assume that a hiker is passing through a forest in which some animal harbors a virus capable of infecting humans, but has not yet done so. The hiker comes into contact with the virus, is infected and dies a couple of minutes later. The virus stops replicating in the deceased hiker and he spreads it to no one else. The epidemic ceases. In this case, a point of equilibrium has been reached.

Another key point is that micro-environments are associated with different points of equilibrium as well, and that these do not necessarily generalize to larger populations. Thus, the environment on the Diamond Princess has one point of equilibrium, the choir in Washington state in which more than half of the members were infected, and the town of Vò, in which 2.9 percent of the population tested positive as the contagion was rampaging in Italy, can be explained without portending dire consequences for the wider world.

Another premise used to explain the observed behavior of the virus is that there is a gradient of resistance to disease spread that steepens as more people are infected. As mentioned previously, this is a generalization of the phenomenon responsible for herd immunity. Not everyone has the same susceptibility to the virus at the same time and for the same type of exposure. It is the distribution of this degree of resistance throughout a population and within a particular environment that determines the points of equilibrium. This was true for the plague of Justinian, the Black Death, the Spanish flu epidemic, SARS, H1N1, the Haitian cholera epidemic, etc., and it will be likely be true for the Wuhan coronavirus.

Coronavirus: the uniformity error

An earlier post on this blog, the one dated 3/24/20 and titled "Coronavirus:predictions," estimated that the total number of coronavirus infections in the U.S. would be about 400,000 and the number of deaths would be about 5,800. These predictions were not very good, and subsequent events demonstrate one reason why. The predictions were made at a time when the the rate of change of observed cases in Washington state was 0.146, while that in New York state was 0.214. At the time of this post, however 49% of the observed cases in the United States are in New York and New Jersey. Obviously, New York and New Jersey do not contain 49% of the U.S. population. One assumption that went into the erroneous prediction of 3/24/20 was that the trajectory of infections in New York would follow that in California and Washington state. In other words. the prediction contained an erroneous assumption of uniformity. If, for example, the current number of total cases in New York was proportional to that in California, the number of cases in New York would be 7,024 instead of the observed 122,031.

This error of uniformity is perhaps the most common and significant impediment to predicting the course of coronavirus spread, and it takes many forms. It is for example, erroneous to assume that everyone is equally susceptible to infection, or that the virus will spread at the same rate among different locations and among different populations. It is an error to try and "extrapolate" from one population to another, or from a small population to a large one. The wilder estimates, those that predicted millions of deaths in the United States, or hundreds of thousands in the United Kingdom were based largely on this error. This error propagates throughout epidemiologic models and unfortunately influences decision-makers into policies that are just as erroneous as the faulty assumption that underlies them.

This error is compounded by another, equally prevalent fallacy, and that is differences in data between two places, say for example, Italy and Sweden, or South Korea and Spain, are accounted for by one or two factors, e.g. testing, or demographics or "not taking the virus seriously." This subsequent folly is dependent on the first. It is assumed that there is uniformity between Italy and South Korea such that if the Italians had done precisely as the South Koreans, they would have had precisely the same outcomes. Simple observation demonstrates that this is foolish, and a more relevant factor is being overlooked.

Another related error is extrapolating a report of a number of people being infected by seemingly trivial exposures into a notion that this is representative of how the infection spreads.

There are a number of observations that appear to be paradoxes that refute the erroneous assumption of uniformity, among them:

- the disproportionate number of cases in New York and New Jersey;
- the relatively high, but absolutely low number of infections in San Marino and n the Diamond Princess;
- the anecdotes of "super spreaders," where a large number of people appear to have been infected by relatively trivial exposures;
- the relatively low prevalence of infection in the Italian town of Vò, and the currently low rate of positive antibody tests in San Miguel County, Colorado.

A reasonable hypothesis regarding how the virus spreads and how best to model it must account for these observations. One such hypothesis has been presented in previous posts and will be expanded upon subsequently

Coronavirus: refining the model

The simple model described in the post from 4/2/20 is an idealized, but unrealistic representation of reality. In fact, we can only observe the data that we measure, in this case by testing people for coronavirus. There is no uniformity as to who gets tested or when, or whether some people are infected, and can spread the virus, yet do not show up in reported statistics. We can make some simple additions to our model to provide, again idealized, methods for incorporating these factors. To do this, we make an assumption that people will mot be tested for coronavirus until some number of days after they are infected. This accounts for incubation period, delay in getting tested once symptoms appear, as well as the lag in obtaining test results.

To do this, we make an educated guess as to a reasonable number of days, call this N, to account for these lags and delays, say for example six days. We then go to our spreadsheet and create a new column which we will begin N+2 rows from the top. In this cell we put the value from the same row of the column representing the new cases, C in our example. However, we also want to account for the fact that not everyone who is infected will be tested or have a positive result. This may be because the test result is a false negative, or because the person never develops concerning symptoms, because of logistic constraints, or social factors, etc. We account for this by multiplying the daily new cases by some factor. for example 0.75. In the cell below we add this value to our adjustment factor times the next daily new case value. Highlight the cell and drag the right hand corner down to the end of our simulation. This column now reflects a modeled population of test positive coronavirus patients. although it assumes no false positive results.

If we do this, we note that the initial ratio of observed daily new cases to total cases overstates the value of r, but as the epidemic proceeds, this value tends to zero while the value of r decays to some baseline number. We also note that, as might be expected the actual peak in the daily new cases occurs N days before the measured peak. this difference is shown in Figure 1 which compares the actual number of new infections (red) per day to the measured daily change in the number of infections; i.e. the numbers that are actually reported (green).

Figure 1.

This gives some insight into the effects of testing, and the various omissions and delays associated with tracking the spread of the virus using reported numbers.