Coronavirus Update III: Secondary Peak and Freak——ing Out

Coronavirus Update III: Secondary Peak and Freak——ing Out

All the good stuff, caveats, and explanations in linked in Update II, so go there first if you haven’t seen it yet.

Signs & Symptoms

Skip to the next section if you want the numbers. Else let’s start with this:

As I pointed out elsewhere, “gaseous plume” is never a cheerful phrase.

Second, to avoid the suspense, the new flu numbers from the CDC (as of 22 February).

CDC estimates that so far this season there have been at least 32 million flu illnesses, 310,000 hospitalizations and 18,000 deaths from flu.

Maybe up to ~20,000 by now. In the USA alone. A crude, don’t-believe-it, useless almost-certainly wrong worldwide estimate is ~300,000 for the year (extrapolating from our population to the world). Anyway, the real number will be higher than 20,000. Coronavirus after a couple of months is 3,000 in the entire world.

CDC flu pic (weeks on x-axis):

On the way down!

Now take a look see at this pic, unearthed by physician Christos Argyropoulos of a similar coronavirus outbreak in Michigan (the best state) back in the 1960s.

This was in a small area with a monitoring program in place. What’s interesting to us is that secondary peak, coming well after the main one. Now this is a small sample, and small samples are variable, but then all numbers are caused, so that this peak is real, we just don’t necessarily know all the causes.

Here’s various flu seasons:

It will be surprising if the coronavirus doesn’t fit this shape.

And as we have been pointing out, SARS was much the same as coronavirus COVID19: an initial peak in the hot zone, followed later by a secondary peak with higher estimated mortality rates outside the hot zone. Canada was particularly hard hit. Washington State may be our Canada.

The double peak we’re experiencing in current cases, to be shown in a moment, isn’t entirely the same kind of thing. We’ll get the secondary outbreak, but with this data we also have this thing called a media-induced panic. This is causing many who ordinarily would not go to get checked, to go to get checked, resulting in many marginal cases added to the total. Look to Italy, which is now testing like mad, and because of that we have a big blip of new casts.

I’ve asked around but I haven’t had anybody chime in on whether the rough tests to diagnose this novel coronavirus, the COVD19, is picking up ordinary cold coronaviruses, and vice versa. Since tests are always imperfect, this has to be happening. I did read that lung x-rays were used in some places as diagnostic, which would misidentify flu, but maybe that’s rumor, and I haven’t been able to rediscover the source.

If the media panic is real what we’ll see is a secondary peak higher than the one we ordinarily expected. The ordinary one is what we’d see when the infection moves out of the hot zone to other areas, usually infecting mostly sicker patients, hence areas outside the hot zone have higher fatality rates. The way we’ll know the secondary peak is hype induced is if fatality rates don’t track.

Of course, fatality rate peaks necessarily lag cases peaks: you have to get sick before you die. So watch for the deaths to start increasing again. You won’t miss it. The media will be right on it.

Incidentally, here’s a story of a 60-some-year-old who got the virus on that cruise ship. He’s doing fine and recommends not panicking. “I breathe easily, and I don’t have a stuffy nose. My chest feels tight, and I have coughing spells. If I were at home with similar symptoms, I probably would have gone to work as usual.”

This Bloomberg writer takes an opposite approach:

In the grip of a new infection spreading around a planet with no natural immunity, it can feel like the sky is falling. Over the coming months, it’s likely that a significant share of the world’s population will experience some of the dread of the Covid-19 coronavirus that people in China have suffered over the past few months. Many will die.

All the cancellations, hoarding, and what not you will have already heard about. My idea is that many companies are ceasing business travel because (a) many other companies are canceling, and (b) if any employee gets sick, it’s lawsuit city. This adds to the hype.

Before we get to the numbers, here’s an excerpt from a new NEJM article on the virus.

On the basis of a case definition requiring a diagnosis of pneumonia, the currently reported case fatality rate is approximately 2%. In another article in the Journal, Guan et al. report mortality of 1.4% among 1099 patients with laboratory-confirmed Covid-19; these patients had a wide spectrum of disease severity. If one assumes that the number of asymptomatic or minimally symptomatic cases is several times as high as the number of reported cases, the case fatality rate may be considerably less than 1%. This suggests that the overall clinical consequences of Covid-19 may ultimately be more akin to those of a severe seasonal influenza (which has a case fatality rate of approximately 0.1%) or a pandemic influenza (similar to those in 1957 and 1968) rather than a disease similar to SARS or MERS, which have had case fatality rates of 9 to 10% and 36%, respectively.

The efficiency of transmission for any respiratory virus has important implications for containment and mitigation strategies. The current study indicates an estimated basic reproduction number (R0) of 2.2, which means that, on average, each infected person spreads the infection to an additional two persons. As the authors note, until this number falls below 1.0, it is likely that the outbreak will continue to spread.

The mortality rate is highest in the elderly and sick, as expected. This is not killing off healthy individuals.

Model Weakness

The naive model we’ve been using is breaking down, since it’s not designed to capture secondary peaks. The total model won’t be too terrible, but the daily cases and deaths will suffer. The cases more than the deaths, since we haven’t got to the secondary peak in deaths yet.

Make sure to use the unlogged y-axis transform, and the secondary peak in the case totals is obvious:

Here’s the daily cases, with the naive model overlaid. Completely missing the secondary peak.

The daily deaths, as we guessed, are so far fine:

These should re-peak in a few days when the worst of the new cases pass on to final judgement. Now I also ran the death rate estimate, which was ramping up to the point of the secondary peak, then began falling, as expected, because we’re adding marginal cases.

Updated model

Here is a piece-wise model, which uses the naive in two segments; i.e. the same logistic model from start to a few days ago, then a new one starting there until now and into the future. I used my eye to pick the point. You can try other points.

This is not a good model: it’s a quick-and-dirty hack and all I had time to do. Maybe by next week I can get something better. Let’s see how it works. Replace the model code with this:

  d.g = 35 # same now for both cases and deaths; step-wise point, chosen by eye
  x.1 = x[1:d.g,]
  x.2 = x[(d.g+1):nrow(x),]
  fit.1 <- nls(actual.cases ~ SSlogis(day, phi1, phi2, phi3), data = x.1)
  fit.2 <- nls(actual.cases ~ SSlogis(day, phi1, phi2, phi3), data = x.2)
  p.cases.1 = predict(fit.1, data.frame(day=1:d.g)) 
  p.cases.2 = predict(fit.2, data.frame(day=(d.g+1):(dim(x)[1]+days.ahead))) 

  fit.1 <- nls(actual.deaths ~ SSlogis(day, phi1, phi2, phi3), data = x.1)
  fit.2 <- nls(actual.deaths ~ SSlogis(day, phi1, phi2, phi3), data = x.2)
  p.dead.1 = predict(fit.1, data.frame(day=1:d.g)) 
  p.dead.2 = predict(fit.2, data.frame(day=(d.g+1):(dim(x)[1]+days.ahead))) 

  l =  length(1:(dim(x)[1]+days.ahead) )
d = seq.Date(as.Date(x[1,1]), length= l, by='day' )
  x[1:l ,1] = d

x$p.cases = c(as.numeric(p.cases.1),as.numeric(p.cases.2))
x$p.dead  = c(as.numeric(p.dead.1),as.numeric(p.dead.2))

The gives these update pictures:

It's a bit early in the secondary peak, so the model has it soaring off into the great beyond. This makes it extremely conservative, forecasting the end sometime in April. This is in line with CDC flu trajectories, which guess about two months more. A nice northern hemisphere warm spell before then would help. Sunlight being the best disinfectant is not just a metaphor.

Cases show a reasonable drop off. We'll see.

Notice we used the same date for the departure point for daily cases and daily deaths, even though we know deaths must lag. Deaths haven't really started to re-peak. The step-two model can be changed in the obvious way when we notice it.

Let's give this new model a week and see how it does.

Clockwise or counter-clockwise

Which direction do you run when panicking?

Look at the numbers inside China. Yes, they may be lying, but, yes, they may be telling the truth. Cities in China are closer to the hot zone than, say, we in the States are.

How many cases in the densely populated Beijing? 413. How many deaths? 8. Two percent. Shanghai, which is closer to Wuhan, has 337 cases, 3 deaths. And this is after months of exposure at the end of winter.

There about 90,000 cases, 80,000 of which are in China. South Korea (where that death cult purposely spread the virus), Italy, and Iran comprise the bulk of the remaining.

The closer to Wuhan, the worse it is. But daily numbers are not increasing as they have been there.

It can't be emphasized enough that flu is worse. But we live with flu and scarcely think of it. When we hear of a flu death, we shrug. It's natural. Not welcome: but part of the backgroun.

Same thing might happen with COVID19. It might seasonally recur. SARS might have, too. Not too likely with COVID19 because the mortality rate is higher than flu. A disease which kills a lot of people fast is more likely to burn out than one that kills many more slowly, like flu. And, yes, the common cold----which is sometimes a coronavirus (not COVID19)---which also kills, but at a low rate.

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  1. Briggs

    If flu has killed ~300,000 worldwide this year, and coronavirus has killed 3,000, then flu is …. 100 x worse.

  2. Bill_R

    18,000/32,000,000 suggests a CFR of roughly 0.06%. Covid is about 2% in the general pop, much higher in my age/comorbidity group. That’s about 30-40x worse. (CFR is, of course, conditional on getting infected.) Time for minimax actions, maybe? I’d like to make it to 90 or more….

  3. Briggs


    These rates by age are probably in the ballpark:

    It’s 15% 80-89, 8% 70-79, 1.3% 50-59, down to 0.4% 40-49, and so on, with no deaths 0-9.

  4. Bill_R

    Thanks. I’ve seen those, too. I’m in the 2nd category, without counting the comorbidity “bonuses”. Haven’t seen any numbers on those yet. Nor have I seen any info on “ancestry bonuses”, other than speculation about Silk Road/Mediterranean groupings being more susceptible to flu and variability in ACE2 receptors. ( You can guess the type of school where I learned Biostat)

    I’d really like to see some information on how specific the diagnoses are, too. When I see “mass testing” I go to “false positives/false negatives” immediately. Having done industrial chemistry in a prior career (like your weatherman times, but as a civilian) I expect that is difficult to control.

  5. Briggs


    Some comorbities on that page, lower down, but not by age. Nothing unexpected, but no genetics.

  6. I’ve been reading lots of stuff about this thing – none of it clearly definitive or trust worthy. Hype aside, it seems there are about equal cases to be made for the extremal “it’s nothing” and “the world is ending” views.
    I’d opt for what I hope is true: that this isn’t a big deal, except that there are some weird things going on. Two examples:
    1 – china’s apparent over reaction. Their view of human life is rather different from ours and I can’t see them shutting down whole cities over a few hundred, or even a few thousand, deaths; and,
    2 – the apparent death rate among senior government people affected in Iran.

    Of course, China is almost certainly lying about nearly everything and Iran is probably not reporting (or even tracking) deaths among the kulaks, but normal epidemilogical models like yours fit the Korean numbers but not the observed political behavior.

    An off-the-wall hypotheses that does fit is that the virus self-attenuates with transmission at a nearly exponential rate. Imagine a 100% death rate among the cleaning staff and lab officials who were the first victims, a 40%+ rate among the second generation (i.e. people who interacted with the lab’s walking dead), etc all the way down to about a 1% rate in the fifth generation.

    Imagine something like this, and both the numbers and the observed behaviors make sense – and may mean that the effect on us will be almost entirely political and economic, rather than medical.

  7. Rollory

    You’re quoting statistics about this out of China as though they were somehow more relevant than a swords’n’sorcery novel.

    To pick one out of a multitude of examples: for at least a week in late January (I didn’t keep track to see if it continued), the number of fatalities the Chinese were reporting was always a mathematically precise 2.1% of the number of new cases they were reporting. Each day.

    This post is innumerate nonsense and needs to be redone from scratch.

  8. Briggs


    I see you didn’t read the mandatory earlier links.

    And don’t forget the numbers might also be right. Evidence for that are the consistent numbers coming out of other countries.

  9. Mark Millward


    Crowe for what looks like well founded virus skepticism – germ theory versus health of bodily terrain. Good Coronavirus specific paper:

    Jon Rappoport for well grounded investigative journalism:

    And OffGuardian for an excellent alternative to MSM (founded by former Guardian commenters who got banned):

  10. Did anyone here find a site of any sort that points at the statistics for China and the “flu”.

    Extrapolating from US data (provided by the CDC), I would suspect that in the area of the greatest outbreak which has a population of 57,000,000 that we would have seen 57,000,000 * 1/10 => 5.7M flus and 5700 deaths from the flu during the same time that the 2700 died of CORVID-19. But that is just applying the numbers put out by the CDC in the US regarding our deaths.

    Will we be able to detect the deaths from CORVID in the death count for China vs prior years?

    In Washington, they tell me that there are 70 confirmed cases of Flu Death. The CDC tells me that somewhere between 18,000 and 48,000 people have died in the US. That suggests that somewhere between 400 and 1100 people died of the flu in Washington. But we also know that something approaching 22,000 people just died in Washington for the same time period.

    I can actually point at a body bag that might have been tied to the flu. Flu went through the house and one person in the upper age bracket died. Death Cert says “natural causes”.

    All of this makes me madly try and point at “Situation Normal, do not go into the fallout shelter”. It also points at “WTF is going on with the numbers at the CDC?”

    I don’t trust the numbers coming out of China. I can’t say I get warm and fuzzy when I read the numbers from the CDC.

  11. Hun

    Your model fits China perfectly. You should have two charts – one for China alone and one for the whole world.

    “It can’t be emphasized enough that flu is worse.”

    I agree, but the usual response is a snarky “It’s just a flu, right?” accompanied with some version of a doomsday prediction and out-of-context anecdotes. This meme is especially irritating, because it is being used to shut down any reasonable debate. Only hype and fear are allowed.

    Thanks for providing a sane analysis, Briggs!

  12. Kalif

    I agree the media can make more damage than the virus, but it doesn’t hurt to err on the side of caution.
    Simply stating that flu is more dangerous than CV is misleading. We know a lot about flu and how it behaves, despite of different strains every year. We know very little about this new thing, comparatively speaking.
    About 40K US citizens die every year in car accidents, but we don’t say that driving in any given year is 20X more dangerous than 911, even though the numbers would suggest so.
    The probability of being struck by lightning may be greater than that of being attacked by a bear, but if we make a mistake of applying it uniformly across the population, it seems like an office clerk in NY and park ranger in Yellowstone have the same chance of becoming a bear lunch. Not even close. One of them should really pay attention and the other one could care less.
    Uncertainty cuts both ways.

  13. Kgaard

    I’m coming around to the “two strains of Corona” theory. Italy is bad and Iran is horrendous. Today nearly 4,000 new cases have been reported — so the secondary spike is threatening to exceed the original count from Wuhan/Hubei.

    At that point, do we say the model has failed? Or is it just a particularly bad secondary spike? There are claims that Iran has 100,000+ sick. Given the sheer percentage of sick among the Iranian elite, you have to wonder … the claim may be right.

    Right now it seems like a bit of a crapshoot whether the US gets one of these super-bad strains like came upon Milan and Iran no? How do we know it won’t happen before the warm weather hits? Lots of Chinese on the coasts.

  14. Dave

    China’s cases only peaked as early as they did because they put over 100M people on lockdown. The trajectory of an outbreak responds to the actions taken. Take no action, get more outbreak.

    SARS and MERS both caused permanent lung damage, and from what I’ve read, that is a risk with this one too.

    And finally, as I’ve stated before: no one has been vaccinated. That’s what makes this potentially more dangerous than the typical flu. Perhaps panic is too much, but concern and precautionary measures seem appropriate.

  15. Kgaard

    Actually the deaths model has technically broken — 202 new deaths yesterday — that’s above the Wuhan peak. I guess it’s possible they were lying about Wuhan and true deaths were higher. But it’s also very possible they are lying about Iran and true deaths are higher.

    To me it looks like the Iranian breakout may be of equal intensity to Wuhan — and Italy is still growing. So the notion that the point of initial breakout is necessarily the most powerful is really being tested here and in the end may not hold up. That has bad implications for the further spread around the planet. If in fact it’s capable of being just as powerful outside Wuhan as inside, then why can’t the US have a breakout of equal intensity as Italy? Or perhaps someone have a vicious breakout next winter?

  16. Dave

    One more comment:

    This blog likes to emphasize decisions, and yet also likes to compare the flu to COVID-19 to downplay the latter. But what’s the decision to be made about the flu? Flu season will end in about 3 weeks, and a flu shot takes about 2 weeks to build up immunity. Plus, nearly everyone already knows they can get flu shots to lower their risk (and help slow spread within the population). Yet, there are still decisions and actions that can be made to lower the impact of COVID-19, which is still growing to some unknown limit and killing people. At the very least, with so few immune to it, we should want to slow its spread so as to not overload hospitals. SARS and MERS were not driven away by seasonality like the flu, and Singapore had a lot of cases in warm weather.

    Sure, most cases have relatively mild symptoms, but as mentioned above, there may be permanent damage in some cases. Any quotes from the people who died about how mild the symptoms are? I don’t say that to promote panic, but there are real consequences to inaction. Personally, I believe that enough Americans will reduce contact and isolate themselves or their families to slow the spread relative to some other countries, but that still requires action, not downplaying the threat.

    Of course, if such actions are successful, some will say, “see, it was never really a threat.” But the counterfactual may have been much worse without the actions. But you can look at the actions of Taiwan compared to South Korea, for differences in results from different actions.

  17. Dave

    I will answer my own question here, as I gave it more thought. The decisions *not* being made about the flu include isolation and other panic, despite it infecting and killing a fair number of people. That’s the contrast. So I take back part of my point on decisions, and rely more on the absence of vaccination (and “herd immunity”) and potential long term damage to the lungs for justifying some of the concern.

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