Math: The (pen)Ultimate Pandemic Reality Check

The combination of initial forays back to the world, work, and notably schools; plus far more testing than we did at the start of the pandemic, produces one inevitable result: surges in case counts everywhere the population wasn’t uniformly exposed already. Is this bad, and if so- how bad? Is it in some way good? Or, is it something in between?
Blackboard covered with mathematical formulas.

To decide, we need a clear and complete understanding of the population impacts of SARS-CoV-2 we have yet to achieve through a fog of inadequate testing, deficient policies, competing passions, and the drama and distortions of social and conventional media alike.

The ultimate resolution to all of this would be population-level data regarding past and current infections, contingent outcomes, and the various expressions of immunity and resistance. The penultimate resolution- and the more accessible to us- is simple math, using the data we do have.

  • Finding it Hard to Manage What We Failed to Measure

Perhaps the greatest deficiency among the consistently deficient U.S. (and to a lesser extent, global) responses to the COVID pandemic– no easy competition to win- has been our lamentable level of testing. We failed to test adequately at the start, and to this day are massively behind where we should be, scrambling, seemingly hopelessly, to make up for lost opportunity.

The damage this has done would be hard to overstate.

For one thing, organizations managing or planning returns to work and school still don’t know what tests to use, for whom, or when, because the nation has failed to establish clear guidance. If they decide independently on tests, they face shortfalls in materials and analyzers because the nation failed to mandate the requisite production and sourcing. Colleagues and I have rolled our eyes over this, reflecting on the phenomenally rapid shifts in American production made to meet the challenges of World War II. We certainly can…we simply haven’t.

More damaging, however, than the failure to generate tests, has been the failure to generate data. Data are to public health and epidemiology what a transparent windshield is to any given plane, train, or automobile. Lack of data is an opaque windshield, and visionless flailing, if not train wreck, that inevitably ensues. Welcome to COVID in America.

We have had no idea how many of us were infected. And accordingly, we have had no idea how dangerous this virus is or isn’t; how likely it is to infect us; how likely to harm us, or in what ways.

Worse still, such benighted flailing is the perfect incubator for extreme anxiety and radical opinion, which in turn invites a steady diet of hype and drama- followed by more anxiety. This cycle has repeated daily for weeks (or lifetimes; the difference has become unclear).

  • Drama, in Lieu of Data

The COVID pandemic is bad, but the COVID infodemic – with the viral propagation of distortion, conspiracy theories, sanctimony, lamentation, innuendo, bravado, and apocalyptic conjecture- is potentially far worse. Not knowing how bad the actual pandemic is, we are at liberty to let our interactions with one another, cyberspace, cabin fever, and a ceaseless media barrage conspire to derive many competing versions of morbid fantasy.

Given the opportunity, media will make hay with this forever, since it plays right to their favored mantra: afflict the comfortable, comfort the afflicted. We will get a day or two of reassuring news about pandemic trends, get nominally comfortable with that, and then… get the breaking news that, just possibly, you can get COVID together with dandruff, athlete’s foot, and pinworm, and that the combination will cause your eyeballs to burst into flames.

All of this supernumerary nonsense and hyperbolic drama is because epidemiology, too, abhors a vacuum. All of this is distortion to populate the void where data ought to be.

The ultimate remedy and reality check is data. The next best thing is math, informed by data. Put the right numbers into a mathematical formula, do the calculations right, and the output is fact, or a very close facsimile. Let’s give fact a try.

  • COVID Math, 101

How many cases of COVID have occurred in the United States to date (9/16/20)? As I write this, the official tally is approximately 6.5 million, and this is not just wrong, but absurdly wrong.

By way of reminder, epidemics are like icebergs: the visible manifestations are just the tip. In the case of COVID, hospitalizations and deaths are readily visible; mild and asymptomatic cases are hidden from view absent the methodical testing we have failed to practice from the start.

A recent publication, aligned with many others before it, indicates that actual case counts in the U.S. are fully an order of magnitude higher than we’ve documented. That would mean not 6.5 million cases, but 65 million cases- or one of every 5 Americans.

As noted, facts issue from valid mathematical operations if- but only if- the correct numbers are plugged into them. The 10-fold figure is probably right, but it would good to verify it. Mathematical estimations become quite a bit more convincing when entirely independent models lead to the same outcome.

In this case, they do.

  • Trust, but Verify

Multiple sources– most recently the New England Journal of Medicine, reporting data out of Iceland- indicate that the infection fatality rate (IFR) for COVID is approximately 0.3%, or less. What would it mean for the roughly 200,000 COVID-attributed deaths in the United States (to date) to conform to this consistent, global pattern?

The algebraic equation for that is: [(0.3%) * X = 200,000].

The solution for X is 67 million. This is, but for rounding, just the same as the 10X number above. These two, fully independent methods, both indicate that the United States is misgauging case counts by an order of magnitude. This is non-partisan, ideology-free math; it is very probably the truth.

Unless…COVID is just ten times more lethal to Americans than anyone else around the world.

  • Maybe SARS-CoV-2 Hates Americans?

There is a scant quantum of plausibility there, because our culture not only condones, but actively propagates for profit, an outrageous burden of heart disease, hypertension, obesity, and diabetes that shifts the COVID mortality risks of the young toward those of the elderly. But such effects fall massively below a ten-fold increase in COVID mortality. There are large burdens of these conditions in Europe, too, so this is not the explanation.

So, yes, Americans are dying unnecessarily where our long-neglected chronic disease epidemic overlaps with COVID– but incrementally more of us, not ten times more of us.

The primary explanation is…we have failed to populate the denominator accurately. The mathematical implications of doing so now are that we have had at least 65 million cases here.

Or perhaps, many more- because there is more math to do.

Studies have consistently revealed that much of the immunity achieved after COVID infection, particularly after mild or asymptomatic infection, is not reflected in the production of the IgG antibodies we capture in seroprevalence research. Much of the immunity is expressed in memory T cells and IgA, and these- we do not measure. In other words, the seroprevalence studies are under-representing case counts, too.

By how much?

In the recent New England Journal of Medicine paper, among even those recovered from symptomatic infection, 10% did not produce measurable IgG. This suggests that case counts are under-represented in seroprevalence research by at least 10%. But the apparent majority of COVID cases are minimally symptomatic or asymptomatic – we knew this already, and it is also the ineluctable implication of 60 million cases in the United States that we never even knew had occurred.

Data suggest that asymptomatic bouts of COVID may fail to produce IgG or result in only fleeting levels. This, in turn, suggests that seroprevalence studies- in New York, or Iran, or on navy ships, or in Iceland– may undercount cases by multiples. Actual case counts may be two times higher if half of those infected don’t make IgG; or 3 times higher if 2/3 don’t.

  • Sorry, More Math…

We don’t know. Conservatively, though, the seroprevalence numbers should apparently be increased by 10% at the very least to better reflect the data patterns on display. The formula for that, using the baseline figure of 67 million cases to date in the U.S. is:

0.9 * X = 67 million. X = 74 million, the revised estimate for nationwide infections to date.

We are still not done.

We have long had evidence, increasing over the span of the pandemic, that many of us who get exposed to SARS-CoV-2 simply do not get infected with it. The reason is apparently native resistance to this germ, resulting from prior exposure to related germs, namely common cold coronaviruses (CCCs). Published data on this topic suggest that up to 90% of us may have prior, native resistance – of one degree or another- to the COVID19 pathogen.

This does not change the “infection” fatality rate, or IFR– because exposure without infection does not change the numbers of us infected. But it does invite us to generate a closely related parameter of my own devising: the MEFR, or “meaningful exposure fatality rate.” It does matter, obviously, to all of our projections about COVID-related risk, if say, half of us exposed in fairly ordinary ways confront this virus with a brisk immune response that simply repels the infection before it occurs. This is much the same as asymptomatic infection, but one incremental step better still.

The population range of values for this native resistance I have been able to glean by canvassing a wide array of sources is roughly 30% to 80%.  If we apply the most conservative quantifier- 40% native resistance- then the total population already “exposed” to COVID is greater than the population infected as follows:

0.7 * X = 74 million. X = 106 million. The fatality rate among those meaningfully exposed- the MEFR- is (200,000/106 million), or 0.19%.

  • Sensitivity to Our Ignorance

Lastly, since we don’t know the exact frequency of missing IgG antibodies after infection, and we don’t know the exact prevalence of native resistance, we can do what is called a “sensitivity analysis:” we can enter into our calculations the numbers at the extremes of the plausible ranges. The epidemiologic truth resides reliably somewhere within the resulting bounds.

At the low end of exposure/case count estimation, we apply 10% as the frequency of missing IgG, and 30% as the frequency of native resistance, as done above. The estimated number of meaningful exposures to date in the US, with or without ensuing infection, is roughly 106 million. This is just about one out of every three of us. As noted above, if this number is valid, the fatality rate among those meaningfully exposed would be 0.19%.

At the high end for exposure/case count estimation, we can apply 50% as the frequency of missing IgG (even this may be too low, but it will suffice), and 80% as the upper frequency of native resistance (this figure has been espoused by scientists with relevant expertise, and is consistent with certain contained outbreaks, notably the Diamond Princess cruise ship– but is controversial).

The estimated number of exposures to date in the US is then:

[(0.5 * 0.2 * X) = 67 million].

Here, X – again, the total number of Americans meaningfully exposed to SARS-CoV-2, whether infected or not- is 670 million. Since that is more than twice as many people as live in America, we know that these numerical inputs must be wrong. Actual levels of prior resistance, and/or post-infectious immunity without measurable IgG, are lower than this.

Often, numbers at the middle of plausible ranges are deemed most probable. In this case, that would mean 30% for missing antibodies, and 55% for native resistance. Those entries give us:

[(0.7 * 0.45 * X = 67 million]. X = 213 million.

What the simple sequence of mathematical calculations, coupled with a sensitivity analysis, gives us is a range within which reality is very likely to fall.

At the low end, 67 to 74 million Americans have likely been infected with SARS-CoV-2 to date, and at least 106 million of us have likely been meaningfully exposed. At the high end, something much closer to all of us have either prior infection, or exposure plus native resistance. The truth- which we will only know reliably in retrospect- is almost certainly somewhere in between. The mid-range value of 213 million is a current best guess.

  • Where Are We Now?

Rising case counts now partly signify the exposure of the formerly unexposed to COVID, and partly signify testing scrambling to catch up with what has been the pandemic reality all along: vastly more of us have been exposed and infected than we have documented.

High case counts, per se, are not the principal worry; the concern should be casualties. Where case counts rise without hospitalizations, complications, or deaths- the pandemic is running its course as harmlessly as we may hope.

Where we see any spike in hospitalizations, we are failing to protect the vulnerable from exposure, and immediate adjustments are warranted.

  • What about Sweden?

One final entry in this numerical reality check. We have all heard about Sweden’s approach to the pandemic, letting the virus run its course without lockdown. We may assume that such an approach potentially exposes the entire population to the virus, give or take some small percentage. If so, Sweden’s national fatality rate – total COVID deaths, divided by their population – has been 0.06%. Applied to the population of the United States, roughly 330 million, 0.06% is 198,000, or roughly the number of deaths we have experienced already. Assuming the lethality of SARS-CoV-2 is comparable among Swedes and Americans, then the toll among Americans compounded by the burdens of lockdown is slightly greater than the toll among Swedes without lockdown.

At least eleven countries have had more deaths per million citizens than Sweden, and the U.S. is one of these.

  • Implications

The United States has certainly not had 6.5 million COVID cases to date; we have had at least ten times that many, and possibly, many more than that. This is a verdict born of dispassion where math meets epidemiology; it is devoid of ideology or agenda.

It means that among those exposed or infected, overall rates of hospitalization, complications, and death are an order of magnitude less than they appear.

It does not mean, however, that we have any cause to start disrespecting SARS-CoV-2.

None of the above calculations changes how it feels to lose a loved one to this contagion, and at this point- many of us have. None of the above changes what a devastating disease this is among those most severely affected.

The implications for policy and the practices of personal protection seem clear to me:

1)   A risk-stratified approach to pandemic management, in the service of total harm minimization, makes even more sense now than it did months ago.

2)   We should be tracking both case counts, and casualty (hospitalization, complication, death) counts. Spikes in case counts are not the “enemy” of public health; spikes in casualty counts are. Where these occur, returns to stricter “lock downs” are warranted, because current practices are exposing the vulnerable.

3)   We should avoid spikes in casualty counts in the first place by continuing strict protections of those at high risk – especially nursing home residents – until community transmission levels fall to near zero and/or a dependable vaccine has been deployed.

4)    The nation, states, employers, and others managing the health of populations should establish COVID-related risk tiers, and direct guidance and policy accordingly. Interactions between risk tiers should always honor the requirements of those at higher risk.

5)   Individuals can and should be forewarned, and thus forearmed, with personalized COVID risk assessment.

6)    A number of the major risk factors for adverse COVID outcomes are fundamentally modifiable with lifestyle; populations (the nation, states, communities, worksites) and individuals should be taking advantage of every opportunity for immediate (and lasting) risk reduction through health promotion.

7)   Masking and distancing do not just prevent viral transmission; even when they fail to do so, they attenuate exposure dose, and thus favor non-infection, or mild infection. These practices thus make sense until community transmission levels fall to near zero.

The ultimate pandemic reality check would be pure data- a level of population testing we have failed to achieve, and clearly will not any time soon. The penultimate reality check is math based on the data we have.

Put reasonable numbers into valid mathematical formulas, and the results are reliably free of drama, dogma, distortion or hype. The results are non-partisan, and directed toward neither comfort, nor affliction. They incline simply, dispassionately toward…truth. What we do with that inclination… is up to us.


This article was first published on LinkedIn.

Dr. David L. Katz     is a board-certified specialist in Preventive Medicine/Public Health.

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