TLDRUpFront: A growing fear in the United States is that COVID-19 may kill millions. This fear is based on an incomplete mental-model of how viruses work fed by COVID-19 reporting that highlights facts in isolation from context and triggering our cognitive biases in how we evaluate risk. This InfoMullet provides a mental model for understanding virus contagions, even within uncertainty, to help understand a variety of scenarios in the United States. The scenarios forecast COVID-19 remains a cause for concern, especially among vulnerable populations, but not panic. Especially when that panic leads to actions that are harmful to self and the community.
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COVID-19 is no longer contained to China or its immediate neighbors. Every day a list of new countries report their “first cases”, “first deaths” or “large increases” in infections. The daily reminder that the current fatality rate in China is near 4% and the constant drumbeats of new infections lead many to jump to a mental model that presumes the virus will spread across the entire population and 4% of everyone will die. But that mental model misses an important part of the structure of viruses. Not all the population will become infected in the first place. Knowing this can shift the mental model from catastrophe to valid, even if serious, rational concern.
This is important if you’ve ever tried to have a reasonable conversation with someone shouting in your face. It’s hard to get a word in edgewise. That’s what happens inside the brain when our perception of risk escalates to panic. One part of our mind starts shouting “buy medical-masks!” or “profile Asians!” neither of which are rational, nor helpful, responses. But when we can shift our mental-models back to a more rational state of valid concern, we can listen to that talking voice reminding us to do the things that are both effective: like being mindful how we touch our face and regularly washing our hands; but also mitigate the unintended consequences like runs on supplies or growing anti-Chinese backlash.
Part of that shift requires understanding the term of a fatality rate in relation to the infectivity rate and also using tools to explore the ambiguity of a novel virus in a meaningful way to make better mental forecasts.
Before getting to that standard disclosures apply. The description of contagions, analysis and forecasting techniques that follows is grossly simplified. This is a fast-moving situation and I’m mainly writing this on Saturday and Sunday. For all I know by the time it’s posted zombies will be running wild. But I’m also not aiming this piece scientists or policy experts who I assume already know what they’re doing. Instead this is aimed at an audience trying to decide which voice to listen to in their head. The one shouting “we’re all going to die, buy masks!” or the quieter voice saying, “You know let’s practice today being mindful of not touching our face and see how that goes first?” And this is why I’m posting this to a blog named for luxurious hairstyle of the late 1980’s and early 1990’s rather than submitting it to peer-review. For all the infectious disease specialists out there shouting this isn’t a perfect representation of information, including my sister, /waves at Megan*, please bear that that context in mind.
The Spread of Contagion
To begin shifting our mental models we need a better understanding of how many of the facts thrown at us by the media work together. In a previous InfoMullet we detailed the system structure of a virus contagion and provided a link to a simulation that explores the dynamics. The term “R0”, pronounced R-naught or R-zero, is an aggregate value assigned to diseases that estimates the extent of contagion a single case can generate by infecting additional people. For example ,a person infected by an R2 pathogen could on average be expected to spread it to two other people while contagious, and each of them would spread it to two more. Obviously if an R0 value is less than 1, then virus will not spread successfully, and the higher the R value the more it spreads. The chart from Popular Science below visualizes the R0 values of numerous more well-known infections.
A Dangerous Game of Dots (1)
R0 values are useful because they aggregate a host of detailed factors into one number. But it’s hard for most people to go from an R0 value to a mental model of a viral spread over time. This is because R0 doesn’t account for the stocks of Susceptible and Infected populations as described in the structure. As more Susceptible people become Infected, there’s less Susceptible people in the immediate proximity of an infected patient to become infected.
The Shape of Contagion’s Spread
To improve that mental model we next need to look at how the rate of contagion changes over time. We do this both by studying historical cases and running computer simulations varying all the parameters. What becomes apparent is that the combination of the R0 value and the draining of Susceptible to Infected results in most cases of a tipping point effect where there’s no longer enough uninfected people in proximity to reliably spread the contagion. The virus burns itself out far before it has infected the entire population. Consider the hypothetical image below which compares a pandemic without intervention with one that has an appropriate intervention:
Learn these shapes, you’ll be seeing them a lot. (2)
The vertical axis is the number of new daily cases. This is a rate-of-change. In a pandemic without intervention #1 the shape of the contagion is a sharp growth up in daily cases followed by an equally sharp collapse. This is because the contagion, left unaddressed, spreads more quickly in the population activating it’s tipping point earlier and collapsing. The intervention case #3 is a shallower curve that actually takes longer to conclude. The difference between the two is the net area under each curve, which would represent the cumulative cases over time. If we were to graph the cumulative cases both would appear as an S-Shaped curve, with the no-intervention scenario resulting in much higher total infected cases.
In the image below we compare the hypothetical daily-case behavior on the left, with an actual chart of Hubei Provinces daily new-cases in the middle and the Hubei Province cumulative cases over time.
When theoretical behavior matches actual behavior that’s good. (2), (3)
Notice how the actual daily-case rate in Hubei follows the growth and collapse pattern of the hypothetical, and the cumulative displays the s-shaped pattern of growth. This behavior over time is important to putting R0 and the SIR model in context to understand what will happen as this virus hits new populations. A sharp rise in daily-new cases from the contagion until the tipping-point within the system is activated and daily-new cases begins declining. The cumulative growth rate of total cases, the combination of all daily-new cases, shifts from continuing to climb and flatten.
Prepare to see this sharp rise in daily-new-cases over and over again in a dozen different countries as media reports on the exponential growth but fails to report the following decline as they’ve moved to another country.
Take for example the headlines blaring that Italy’s “cases have jumped by 50% in one day!”(4) Italy is now in the exponential growth part of the growth and collapse pattern. As discussed in the first InfoMullet, COVID-19 had a doubling period every ~2days during that exponential growth. I’m not great at math but 100%/2 days = 50%/day so really what this headline is telling us is that the growth pattern is similar to what we’ve already seen in Hubei. And since Hubei province has more people in it than all of Italy (65M vs. 60M) that headline might as well say “Italy matches Hubei’s pattern – expect contagion to burn itself out in 2 months with ~65K cases 80% of which will be mild and total deaths to be under 2,000.” Because that’s the likely pattern in Italy if it matches Hubei, and we don’t give them any credit for knowing this was coming. It’s not a happy headline to be sure, but it also gives a fuller context than an ominous “Cases growing by 50%!” which is only describing the left hand of that chart pattern.
We’re already seeing in the chart below that global daily cases is beginning its upward ascent, a combination of every country’s growth patterns combined into one chart. But this is worth bearing in mind – if the growth pattern is the same as we’ve seen before in Hubei, why would we expect there not to be a subsequent collapse of daily new cases, leading to a cumulative flattening at the top of the s-curve?
This is what the start of a growth & collapse behavior looks like but #SpoilerAlert it won’t grow like this forever. (3)
This common behavior gives us a crude napkin math number we can use for scenario analysis around the fatality rate. Which is the total number of total infected population when these two patterns have played out. If we take the number of cumulative cases at the tail of the s-curve pattern and divide that into the total population at risk, we have a very crude but useful infection rate as a percentage of the overall population. And that’s the important number to improve our mental models of how this might impact the United States in terms of fatality, and down-shift from “millions will die” panic to “this is serious, but we can handle it” reason.
From Napkin Math to Ambiguous Napkin Scenarios
Using this crude rate of infection as a percentage of the population, we can combine it with the other data that the WHO reported out of China last week and begin forecasting several scenarios for COVID-19 in the United States. These scenarios are notional because we’re working in an ambiguous environment.
We don’t know if the data coming out of China is reliable or consists of under-reporting of either total infections, fatalities, or both. So that’s the element I’m going to vary in these analyses. The intent is to create a range of scenarios, using the crude infection rate as a % of population value, to show that even in the worst case scenarios where China is under-reporting, and our estimates are way off, we still don’t result in a mass-extinction event in the United States.
In the scenarios below I use a simple formula which is Population Size * Infectivity Rate. This provides a “Total Infected” value that is then distributed between Mild, Severe, and Critical Cases based on WHO reporting. These are described as:
80% Mild: anything from cold-like symptoms to that flu-like feeling of being hit by a truck.
15% Severe: Pneumonia, shortness of breath that can land you in the hospital. And
5% Critical: Patients coming down with multi-organ failure, respiratory failure or septic shock.”(5)
Last a fatality rate is applied to the total population of infected cases to show how many people of those infected died. These values are then projected from China onto the United States to give a range of outcomes.
The baseline scenario is based on what we know from JHU’s reporting on the outbreak in Hubei Province.(6) The net infectivity rate is 1/10th of one percent – or .1%. This is determined by dividing the reported cases of 65,000 into the total population of Hubei province of 65,000,000. The fatality rate of 4.1% is obtained by dividing known deaths into the infected population of Hubei. These values are then applied to a US population to create an estimate of the total cases, and the distribution between mild, severe, and critical. And finally, a rough estimate of deaths in the United States.
The base case which assumes accurate Hubei data and projects that onto the United States.
From this first case we now have a very rough baseline we can compare against a range of scenarios of how China may be under-reporting infections, deaths, both, and the location of where victims are concentrated. This allows us to assess, holding all else constant, a range of scenarios given the ambiguity of what we know establishing low and high rough estimates. These scenarios also illustrate the crucial dynamic that napkin math of infectivity rate plays in determining the overall impact, and why the mental model many have been forming in their heads is off by an order of magnitude.
CASE #1: Under-Reporting in Infections
The first ambiguity case assumes that China has under-reported infections by ten-fold. This may not be intentional. If 80% of the cases are mild there may be a great number of infected patients in Hubei that stayed home and did not report to a hospital. But this case assumes that deaths have been reported accurately. Which makes some sense, since it’s more likely that a death would be reported than a mild case of cold-like symptoms. To help highlight changes, we’ve color coded the chart to show what has gotten better, worse, or stayed the same to the baseline. Let’s see what happens.
We modify the case to assume Hubei total infected is being under-reported by 10x.
Notice what happened when we increased infections but held deaths constant? The total cases jumped ten-fold, and increased the number of patients suffering from mild, severe, and critical cases accordingly. But if we assume the death count is accurate, then the fatality rate actually declines to 1/10th it’s previous rate, from 4.1% to .41%. And the deaths stay the same. This can be counter-intuitive at first but makes sense. The fatality rate can only be calculated by dividing deaths into an infected number, and if our infected number was off by being too small, then the fatality rate is going to decline.
Don’t mistake what this chart is saying – with over 500,000 severe and critical cases of COVID-19 in the US that still generates a large health impact and economic impact. But it’s not as bad as people might be fearing.
CASE #2: Under-Reporting of Infections & Deaths
What if China is under-reporting both infections and deaths by a factor of ten? This represents an ambiguity nightmare, where the data we are using is off by an order of magnitude.
We assume both total infections and deaths are under-reported by 10x in Hubei and project that onto the US.
Not surprisingly if both infections and deaths are under-reported by a factor the numbers increase ten-fold: total infected, mild, severe, critical and fatalities all increase. The infection rate goes from 1/10th of a percent to one percent and the fatality rate remains the same at 4.1%. Why does the fatality rate remain the same? Because when the denominator and the numerator of Hubei infected/deaths both increase by ten, the ratio remains the same. 26,665/650,000 = 4.1%
And importantly when we move over to the United States that 4.1% is not applied to the entire US population of 330,000,000. But only the 3.3M who have been infected. This is the key of using a fatality rate only in combination of some understanding of the total population infected and represents the key error in many mental models that are predicting millions upon millions of deaths.
This isn’t to say that COVID-19 does not have a significant health impact on the United States. At 135k deaths that’s more than double the worst-case flu season death rate in recent memory, 80K IN 2018. (7) And we’re still talking over 500K people visiting the hospital with severe or critical conditions. But even there we need to distinguish between “severe” and “critical” using the definitions of the WHO. I’ve seen reports conflating both numbers, comparing it to available ICU beds and predicting the United States will run out of hospitalization space. But the “severe” as bad as it sounds, by definition, is not a hospitalization and should not be included in that number.
CASE #3: Under-Reporting in Deaths but Accurate Reporting of Infections
But what happens if China has the infections accurate, but is under-reporting the deaths? Reversing the ambiguity in Case #1. In scenario #3 we assume there are ten-times as many deaths as reported, but everything else stays the same.
We assume infections are accurate but deaths are under-reported by 10x in Hubei.
In this case the fatality rate increases to a whopping 41%. And the total estimated deaths in the US increase ten-fold, accordingly, reaching the same levels as Case #2. The overall impact remains smaller than #2 in that there are less people overall infected, but the fatality rate among those infected is much higher. Keep in mind the only thing we’re varying in these cases is the ambiguity around China’s reported numbers. There’s a good argument to make that other variations will influence the fatality rate: access to care, healthcare supplies, medicines and other matters of infrastructure and policy response. But in this scenario we’re assuming that the US medical response is no better than China, in order to isolate the effect of ambiguity in reporting.
CASE #4: Concentration of Infected is based in Wuhan and not Spread evenly across Hubei Province
Another kind of misunderstanding is to assume that all 65,000 cases are spread evenly within Hubei’s 65M population. The epicenter of the original outbreak however was Wuhan city, with a population of 11M. So, in this scenario we look at what changes if 80% of all Hubei’s cases, a number I arbitrarily picked, are from within Wuhan. This change in distribution increases the infectivity rate representing more people getting sick from a smaller population and has ramifications for the US case.
By concentrating infected into a smaller population, focused on the city of Wuhan, we increase the infectivity rate from 1/10th of one percent to 5/10th’s of one percent. Applying these estimates to a United States example we obtain a mid-range point between the Base Case and CASE #1.
We assume the distribution of cases is not even across Hubei, and instead 80% are concentrated in Wuhan.
We can now compare all the scenarios side by side and locate COVID-19 risk with a relative comparison to our own annual influenza risk in the United States as reported by the CDC. And just to satisfy that shouting voice in the head I took the Case #2 and multiplied its result by a factor 2-3 times worse than it it already was. What that means is our information isn’t just a little wrong, it’s off by a factor of x20-x30. To repeat Case 5 is taking the worst case scenario and tripling our uncertainty to give an outer range of “we really got this wrong.” I don’t think Case 5 is particularly likely. But sometimes in ambiguity analysis it’s best to take your worst case and just double or triple it to see what happens, and realize it’s still much worse than the mental-model we’ve envisioned. I’ve also included the annual flu season estimates from the CDC, 2010-2018 (7), so we have something to compare these numbers against.
Comparing Base Case & five scenarios against annual flu averages in US.
We see that the range of ambiguity in China’s reported data results in scenarios that are both much less, and more, than the annual flu season. But in no case do we result in millions of deaths. Even the one where our understanding of the data was off by 20x-30x.
Confounding Orders of Magnitude
Of course, the reporting quality of China isn’t the only form of ambiguity we’re dealing with COVID-19. There’s a range of things we just don’t know yet that could make it worse. As a novel virus we don’t know for example if it sustains itself in animal reservoirs allowing it to re-emerge periodically or has a high rate of reinfection. Either scenario may turn that growth & collapse behavior mode above into a repeating period of peaks, and the s-curve of the cumulative cases begin to look like a staircase.
Accepting there is a down-side risk means we should accept there’s an upside risk, that things will be better. Both the infection rate and fatality rate of 4.1% in Hubei represents an overwhelmed healthcare infrastructure at the epicenter of a brand-new virus. Fatality rates in other parts of China have been less and its reasonable to assume that in developed countries with time to prepare it will be even less. Containment measures, once prepared, can better dampen the sharp upward growth. We may see many growth patterns in countries look more like the successful intervention path than the expontential growth and collapse. The identification, mass-production, and deployment of vaccines could place an outer limit on the time horizon that this virus remains truly “novel.”
But let’s discuss the downside risk because that voice in your head isn’t screaming O Happy Day! because it’s concerned about better-than-expected outcomes. One way to compare the impact of ambiguity is to compare the change in the outcome as error in estimate increases. I’m using simple orders of magnitude that are multiplicative, not logarithmic. So, a “10x” means that the order of magnitude is ten times great than what it’s being compared too. Consider the below chart, which compares orders of magnitude between the error in the estimate with a change in magnitude of deaths in the US relative to the flu season.
Comparing order of magnitude changes in error vs. order of magnitude changes in outcomes.
What this chart shows is that even as the error in the estimate rises sharply as an order of magnitude, the magnitude difference in relative death rate relative to the worst recent flu season in 2018 does not rise at the same rate. Even in the extreme case where we’re off by a factor of 20-30x the outcome is only 4.5-6x worse than the annual flu season. And the closer to accurate we are, the impact will be less likely.
Why all the Dread?
So why is there so much dread around COVID-19? Because most humans don’t go through a 3,200 word analysis of virus structures, known data, and ambiguity scenario forecasting before reaching a decision on how to feel. They mainly ask: “does this thing scare me or not?” Part of the fear factor of COVID-19 is that as humans we often use heuristic short-cuts to evaluate risk because it’s cognitively easier than the above exercise. And COVID-19 is hitting a lot of those buttons.
Crowding-Out Effect: We begin with the two shouting voices in our head. Without practice and training it’s easy at points of high emotion for that very loud voice to ‘crowd out’ rational thinking.(8)
Repetitive Exposure: The more stories we see on a topic the more we think it’s an important thing to pay attention too. And right now, media channels are saturated with COVID-19 reporting. We here at the InfoMullet are proud to say, “I’m doing my part!”(8)
Novelty: We pay more attention to threats that are new than threats we are familiar with. As discussed above COVID-19 may be less, about the same, or worse than a regular flu season. And all estimates are much less than the normal leading causes of death in the United States: cancer, heart disease, diabetes etc. Beginning Friday night Turkey and Syria started a regional-power conflict in Syria and I still can’t get anyone to notice. Why? Because we’ve been hearing about war in Syria for eight years now, and even though this state-on-state conflict is substantively different our minds tune it out. (But if you want to know more check out this 1hr Facebook live video where I explained the situation, context and regional actors. We’re also tracking daily updates over on the InfoMullet.)
Involuntary Risk: When we are not able to voluntarily accept a risk, it is forced upon us, we can evaluate that risk up to a 1,000 worse. (8) Walking the plank 20-30’ above the water is a punishment in a pirate movie but leaping out of a perfectly good airplane 10,000’ up is a sign of adventure. Because the former is forced on us and not the latter.
Exotic Effect: In the United States we have a bad habit of ‘othering’ anything that comes from a foreign land. Sometimes this is silly, like our fondness for Acacia berries as health miracles because we imagine them being grown on some exotic mountain slope in South America versus the blackberries that grow in the stickers out back. In many other cases this is exotic effect is based on historical racism of seeing the ‘foreign other’ as barbarous, sinister or dangerous. The virus originating in China has triggered this exotic effect. Imagine for instead this was named the Ankeny, Iowa Virus, later renamed by the WHO “Oh for the Fun-19.” No one care. Because no one ever cares what happens in Ankeny, Iowa and for good reason.
Stock Market Effect: In most developed countries the level of that nation’s key stock market indices serves as a barometer of confidence in the state of things. This varies by country, and as I’ve stated before, stock market values are not reliable indicators of the economy. But as a short-hand measure, there’s few things more accessible that will be regularly reported to large populations than stock market movements. And because COVID-19 is causing a shock to the global market system the stock market indicators have been flashing “Panic! Panic! Panic!” all week. Because the stock-market effect is in a different area: economics vs. health it can be mistaken as a corroboration from an independent source of concern.
The result of all these cognitive triggers going off at once is the shouting voice takes the wheel and we make rash, uninformed, and unhelpful decisions. Take for instance the run on purchasing medical masks. The irony here is that medical masks don’t really protect one from getting infected, you need a respirator for that. And unless you’re actually trained on how to use the mask, or respirator properly, it won’t work. These devices are intended for use by the infected, and the healthcare workers supporting them, who are trained in their use and most at risk of exposure. (9)
It got so bad that over the weekend the Surgeon General had to plead with Americans not to buy the thing that wouldn’t help so there would be some leftover for when it was needed.(10) Because although there are many other valid reasons for using medical masks at the margins, it’s a good bet that people who are deciding to buy them as a fear response, and then forget they have them or forget to use them or use them wrong aren’t just harming themselves. Those supplies are not going to be available to the healthcare workers, infected and population segments that do have valid reasons to use them. And this run on supplies is just one example of an unintended consequence of a fear response run amok.
Why we adjust our Mental Models
The purpose of this article is not to convey false assurances or tell folks to calm their self-identified bits. Learning to shift our mental model of the world from one point of view to another can introduce a break in the shouting match between emotion and reason going on in our head. Because reason has something to say here that’s useful as well.
And that is that COVID-19 is not Ebola, the Black Death, Smallpox or any of nature’s most vicious diseases in a new and unexpected form. It’s an virus from the coronavirus family of viruses we know well in a novel form. And because we know the structures of factors like R0, infectivity rate at the end of the s-curve growth pattern and fatality rate interact, we can use that knowledge to create estimates, even in areas of ambiguity because we’re uncertain how accurate reports from China are.
We know that if China under-reporting the total infections, but accurately reporting the deaths, the fatality rate drops. And if China is accurately reporting total infections but under-reporting deaths we have a more severe contagion, but focused on a smaller population than some might fear. Only if China is under-reporting total infections AND deaths, even by a factor of 10x – does COVID-19 healthcare impacts move well above an annual flu. And even if we double or triple that risk, it becomes a significant healthcare event – but not millions of dead.
Listen to the Quiet Voice – It’s Giving you Good Advice
Shifting to this adjusted mental-model quiets the shouting voice so we can listen to the quiet one and hear what it’s saying.
We hear that voice saying that COVID-19 is conveyed by small droplets of moisture expelled by a sneeze. They travel between 8-10’ at most before landing on the ground and will last on metal or fabrics for 12 hours or more. The route of infection is when we touch one of those droplets and then put our hands and grubby fingers into our eyes, nose, or mouth.
And then that voice asks us two very important questions:
When was the last time we practiced a mindful intention of consciously not touching our face until we had vigorously washed our hands?
When was the last time we practiced regularly and vigorously watching our hands frequently?
These two acts can do more to limit the spread and mitigate the impact than buying a life-time supply of medical masks. Which is important, because nothing in this article should be taken to say that we should just ignore COVID-19. But as in all scenarios of high alarm we need to be careful to do the right thing, and not just “do anything” because our fear is demanding action.
COVID-19 is going to harm vulnerable populations, both here and abroad, to a greater extent than it does affluent ones. We should focus our efforts on helping them where we can. And if our understanding is off 20x-30x it may be much worse than the worst flu season in recent memory. But it’s not going to result in millions of Americans dead and if we let that be our mental model we’ve already surrounded the ground to the shouting voices in our head.
- In the Clancy household two horsemen of the apocalypse are represented by two separate, yet equally important siblings. A real doctor, who diagnoses and cures disease. And an academic all-but-dissertation “doctor” who shakes a tin cup for grant money while studying violence and instability. These are their stories. DUN DUN
(7) https://www.cdc.gov/flu/about/burden/index.html and https://www.statnews.com/2018/09/26/cdc-us-flu-deaths-winter/