Various graphs for deaths from COVID-19, so far

I wrote that I would show you what various graphs of various types of simple models look like for deaths so far due to the current corona virus: linear, exponential, polynomial, and so on. I think that a fourth-degree (not third-degree, like I wrote earlier) seems to fit the data best so far, and that’s better than exponential growth.

First, let’s look at a straight-line best-fit model, superimposed by Excel on the data. (Note: deaths are on the Y, or vertical, axis; the X-axis represents days since the beginning of March. So today, the 6th of April, is day 37 (31 + 6). The dotted red line represents the line of best fit, and the blue dots are the CDC-announced numbers of deaths so far.

is it linear

As you can see, the straight dotted line doesn’t fit the data very well at all. R-squared, known as the correlation coefficient, tells us numerically how well it fits. If R or R^2 equals 1.000, then you have absolutely perfect correlation of the data to your model. Which we do NOT have here. By the way, in that model, then by mid-June we would have about 22,000 dead from this disease.

OK, let’s look at an exponential curve-of-best fit next:

is it exponential

As you can see, this red curve fits the data a LOT better, and R-squared is a lot higher.


We do NOT WANT EXPONENTIAL GROWTH OF THIS OR ANY OTHER DISEASE, BECAUSE IT MEANS WE ALL GET IT! In fact, if this model is accurate and isn’t slowed down, then by mid-June, just plugging in the numbers, we would have 3.3 BILLION (not million) people dead in the US alone. Fortunately, that won’t happen.

BUT there are some parts of the data where the curve doesn’t fit perfectly — let me point them out:

is it exponential -2

At the upper right-hand end, the red dotted line is quite a bit higher than the blue dots. Fortunately. And near the middle of the graph, the blue dots of death are higher than the red line.

OK, let’s look at some polynomial models instead:

is it a second degree polynomial

This is a fancy version of the simple y=x^2 parabolas you may have graphed in Algebra 1. Once again, this doesn’t do a terrific job of conforming to the actual data. At the right-hand end, the blue dots of death are higher than the curve. In addition, if we continued the red curve to the left, we would find that something like two thousand people had already died in the US, and presumably came back to life. Which is ridiculous.

However, if this model were to hold true until mid-June, we would have 127 thousand dead. Not good.

Let’s try a third-degree polynomial (a cubic):

is it a third degree polynomial

That’s pretty remarkable agreement between the data and the equation! That’s the equation I was using in my earlier post. The R-squared correlation is amazing. Unfortunately, if this continues to hold, then we would have about 468 thousand dead in the US.

Let’s continue by looking at a fourth-degree polynomial curve fitted to the data:

is it a fourth degree polynomial

That is an amazingly good fit to the data! Unfortunately, let’s hope that it won’t continue to fit the data, because if it does, then we are looking at a little over a MILLION dead.

Let’s hope we can get these totals to level off by physically distancing ourselves from other households, washing our hands, and getting proper protective garments and testing technology to our medical personnel.


Here’s another model that unfortunately does NOT work: logarithmic growth. If it were the case, then we would have about 10,700 deaths by mid-June.

is it logarithmic


Is Covid-19 Growing Exponentially or Polynomially?

The short answer is, I don’t know.

Exponential growth, in the long run, is much worse. Of course, in the long run, exponential growth of any disease (or anything else in the real world such as Ponzi schemes, compound interest) becomes impossible, because whatever-it-is runs out of people (or whatever) to infect.

I am not a real statistician, but I’ve tried plotting the numbers of reported US cases of COVID-19 and of fatalities against the date (starting March 13), and asking Excel and my TI-84 calculator to calculate and graph various “trendlines” (or correlations) using linear, logarithmic, exponential, power, and polynomial models — curves that you might have studied in math class.

Bad news: the graph is DEFINITELY not linear (that is, the points do NOT lie on a straight line, and the number of cases and deaths so far are NOT rising by the same amount each day).

I tried exponential growth, wherein the number of cases/deaths increases at the same RATIO (or percentage) each day. GOOD NEWS: those numbers don’t fit very perfectly. (I’ll show you graphs later.) the plotted points, recently, lie BELOW the exponential curve of best fit. YAY!

What fits best so far is polynomial growth with degree 3 or 4. (Using figures up thru yesterday, I get F=1.256*d^3 – 68.18*d^2 + 1245*d – 7447, where F means the number of Corona virus fatalities in the US and d is the number of days starting from March 1.)

Not that polynomial growth is something we want to continue!

If it did, and the current polynomial-of-best-fit continues to work, then by my calculations, we would have about half a million dead in the US alone by the middle of June.

And not that my model has any fundamental validity — after all, if you plug in d=0, ie February 29, you get that there were NEGATIVE 7,457 fatalities from the new Corona virus which is absurd.

However, the fact that the curve is showing less than strictly exponential growth is good. Now, if we could get EVERYBODY to take physical-social distancing seriously, AND get needed supplies and tests to hospitals and clinics, we could beat it down to zero.

Published in: on April 6, 2020 at 4:42 pm  Leave a Comment  

Captain Crozier’s Letter

Here is a link to the text of the letter written by the recently-fired captain of the aircraft carrier Theodore Roosevelt. It does not sound unhinged or emotional to me.

or else try this one.

(Edit: the previous link didn’t work well. Let me know if these work better.)

Who’s getting the $2 trillion?

Some simple math with some large numbers leaves me with a big question.

Assume that about 330,000,000 Americans each get a full $1,200 stimulus check (which isn’t all that much). Multiply those numbers and you get about $400,000,000,000, or $400 billion. But the stimulus package supposedly totals about five times as much as that, or roughly $2 trillion.

So individuals are only receiving one-fifth, or 20%, of the stimulus package.

My son runs a small business. I haven’t heard of any relief for firms like his.

Should I conclude that large corporations are getting the other 80% of this stimulus?

If not, what am I missing?

Published in: on April 4, 2020 at 3:25 pm  Comments (2)  

Head of Chinese CDC gives interview to Science magazine on COVID-19

His name is George Cao; among other places, he studied at Oxford and Harvard.

Q: What can other countries learn from the way China has approached COVID-19?

A: Social distancing is the essential strategy for the control of any infectious diseases, especially if they are respiratory infections. First, we used “nonpharmaceutical strategies,” because you don’t have any specific inhibitors or drugs and you don’t have any vaccines. Second, you have to make sure you isolate any cases. Third, close contacts should be in quarantine: We spend a lot of time trying to find all these close contacts, and to make sure they are quarantined and isolated. Fourth, suspend public gatherings. Fifth, restrict movement, which is why you have a lockdown, the cordon sanitaire in French.

Q: The lockdown in China began on 23 January in Wuhan and was expanded to neighboring cities in Hubei province. Other provinces in China had less restrictive shutdowns. How was all of this coordinated, and how important were the “supervisors” overseeing the efforts in neighborhoods?

A: You have to have understanding and consensus. For that you need very strong leadership, at the local and national level. You need a supervisor and coordinator working with the public very closely. Supervisors need to know who the close contacts are, who the suspected cases are. The supervisors in the community must be very alert. They are key.

Q: What mistakes are other countries making? 

A: The big mistake in the U.S. and Europe, in my opinion, is that people aren’t wearing masks. This virus is transmitted by droplets and close contact. Droplets play a very important role—you’ve got to wear a mask, because when you speak, there are always droplets coming out of your mouth. Many people have asymptomatic or presymptomatic infections. If they are wearing face masks, it can prevent droplets that carry the virus from escaping and infecting others.

Q: What about other control measures? China has made aggressive use of thermometers at the entrances to stores, buildings, and public transportation stations, for instance.

A: Yes. Anywhere you go inside in China, there are thermometers. You have to try to take people’s temperatures as often as you can to make sure that whoever has a high fever stays out.

And a really important outstanding question is how stable this virus is in the environment. Because it’s an enveloped virus, people think it’s fragile and particularly sensitive to surface temperature or humidity. But from both U.S. results and Chinese studies, it looks like it’s very resistant to destruction on some surfaces. It may be able to survive in many environments. We need to have science-based answers here.

Q: People who tested positive in Wuhan but only had mild disease were sent into isolation in large facilities and were not allowed to have visits from family. Is this something other countries should consider?

A: Infected people must be isolated. That should happen everywhere. You can only control COVID-19 if you can remove the source of the infection. This is why we built module hospitals and transformed stadiums into hospitals.

Q: There are many questions about the origin of the outbreak in China. Chinese researchers have reported that the earliest case dates back to 1 December 2019. What do you think of the report in the South China Morning Post that says data from the Chinese government show there were cases in November 2019, with the first one on 17 November?

A: There is no solid evidence to say we already had clusters in November. We are trying to better understand the origin.

Q: Wuhan health officials linked a large cluster of cases to the Huanan seafood market and closed it on 1 January. The assumption was that a virus had jumped to humans from an animal sold and possibly butchered at the market. But in your paper in NEJM, which included a retrospective look for cases, you reported that four of the five earliest infected people had no links to the seafood market. Do you think the seafood market was a likely place of origin, or is it a distraction—an amplifying factor but not the original source?

A: That’s a very good question. You are working like a detective. From the very beginning, everybody thought the origin was the market. Now, I think the market could be the initial place, or it could be a place where the virus was amplified. So that’s a scientific question. There are two possibilities.

Q: China was also criticized for not sharing the viral sequence immediately. The story about a new coronavirus came out in The Wall Street Journal on 8 January; it didn’t come from Chinese government scientists. Why not?

A: That was a very good guess from The Wall Street Journal. WHO was informed about the sequence, and I think the time between the article appearing and the official sharing of the sequence was maybe a few hours. I don’t think it’s more than a day.

Q: But a public database of viral sequences later showed that the first one was submitted by Chinese researchers on 5 January. So there were at least 3 days that you must have known that there was a new coronavirus. It’s not going to change the course of the epidemic now, but to be honest, something happened about reporting the sequence publicly.

A: I don’t think so. We shared the information with scientific colleagues promptly, but this involved public health and we had to wait for policymakers to announce it publicly. You don’t want the public to panic, right? And no one in any country could have predicted that the virus would cause a pandemic. This is the first

Q: It wasn’t until 20 January that Chinese scientists officially said there was clear evidence of human-to-human transmission. Why do you think epidemiologists in China had so much difficulty seeing that it was occurring?

A: Detailed epidemiological data were not available yet. And we were facing a very crazy and concealed virus from the very beginning. The same is true in Italy, elsewhere in Europe, and the United States: From the very beginning scientists, everybody thought: “Well, it’s just a virus.”

Q: Spread in China has dwindled to a crawl, and the new confirmed cases are mainly people entering the country, correct?

A: Yes. At the moment, we don’t have any local transmission, but the problem for China now is the imported cases. So many infected travelers are coming into China.

Q: But what will happen when China returns to normal? Do you think enough people have become infected so that herd immunity will keep the virus at bay? 

A: We definitely don’t have herd immunity yet. But we are waiting for more definitive results from antibody tests that can tell us how many people really have been infected.

Q: So what is the strategy now? Buying time to find effective medicines?

A: Yes—our scientists are working on both vaccines and drugs.

Q: Many scientists consider remdesivir to be the most promising drug now being tested. When do you think clinical trials in China of the drug will have data?

A: In April.

Q: Have Chinese scientists developed animal models that you think are robust enough to study pathogenesis and test drugs and vaccines? 

A: At the moment, we are using both monkeys and transgenic mice that have ACE2, the human receptor for the virus. The mouse model is widely used in China for drug and vaccine assessment, and I think there are at least a couple papers coming out about the monkey models soon. I can tell you that our monkey model works.

Q: What do you think of President Donald Trump referring to the new coronavirus as the “China virus” or the “Chinese virus”?

A: It’s definitely not good to call it the Chinese virus. The virus belongs to the Earth. The virus is our common enemy—not the enemy of any person or country.

Published in: on March 30, 2020 at 12:13 pm  Comments (2)  

A new batch of Billionaire-funded flacks for education privatization

Tom Ultican has done some research and has discovered a brand-new crop of bought-and-paid-for AstroTurf groups and spokespersons, all dedicated to fighting teacher unions, bloggers like me, and the very concept of a free, integrated, public school system. Many of the groups and individuals he’s noting are ones I was completely unfamiliar with, and maybe to my readers as well.

Here is the link.

I definitely need to follow Ultican’s blog.

Published in: on March 29, 2020 at 11:14 am  Leave a Comment  

Paul Krugman on Zombie Ideas

Covid-19 Brings Out All the Usual Zombies

Why virus denial resembles climate denial.

By Paul Krugman

Let me summarize the Trump administration/right-wing media view on the coronavirus: It’s a hoax, or anyway no big deal. Besides, trying to do anything about it would destroy the economy. And it’s China’s fault, which is why we should call it the “Chinese virus.”

Oh, and epidemiologists who have been modeling the virus’s future spread have come under sustained attack, accused of being part of a “deep state” plot against Donald Trump, or maybe free markets.

Does all this give you a sense of déjà vu? It should. After all, it’s very similar to the Trump/right-wing line on climate change. Here’s what Trump tweeted back in 2012: “The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing noncompetitive.” It’s all there: it’s a hoax, doing anything about it will destroy the economy, and let’s blame China.

And epidemiologists startled to find their best scientific efforts denounced as politically motivated fraud should have known what was coming. After all, exactly the same thing happened to climate scientists, who have faced constant harassment for decades.

So the right-wing response to Covid-19 has been almost identical to the right-wing response to climate change, albeit on a vastly accelerated time scale. But what lies behind this kind of denialism?

Well, I recently published a book about the prevalence in our politics of “zombie ideas” — ideas that have been proved wrong by overwhelming evidence and should be dead, but somehow keep shambling along, eating people’s brains. The most prevalent zombie in U.S. politics is the insistence that tax cuts for the rich produce economic miracles, indeed pay for themselves, but the most consequential zombie, the one that poses an existential threat, is climate change denial. And Covid-19 has brought out all the usual zombies.

But why, exactly, is the right treating a pandemic the same way it treats tax cuts and climate change?

The force that usually keeps zombie ideas shambling along is naked financial self-interest. Paeans to the virtues of tax cuts are more or less directly paid for by billionaires who benefit from these cuts. Climate denial is an industry supported almost entirely by fossil-fuel interests. As Upton Sinclair put it, “It is difficult to get a man to understand something when his salary depends on his not understanding it.”

However, it’s less obvious who gains from minimizing the dangers of a pandemic. Among other things, the time scale is vastly compressed compared with climate change: the consequences of global warming will take many decades to play out, giving fossil-fuel interests plenty of time to take the money and run, but we’re already seeing catastrophic consequences of virus denial after just a few weeks.

True, there may be some billionaires who imagine that denying the crisis will work to their financial advantage. Just before Trump made his terrifying call for reopening the nation by Easter, he had a conference call with a group of money managers, who may have told him that ending social distancing would be good for the market. That’s insane, but you should never underestimate the cupidity of these people. Remember, Blackstone’s Steve Schwarzman, one of the men on the call, once compared proposals to close a tax loophole to Hitler’s invasion of Poland.

Also, billionaires have done very well by Trump’s tax cuts, and may fear that the economic damage from the coronavirus will bring about Trump’s defeat, and hence tax increases for people like them.

But I suspect that the disastrous response to Covid-19 has been shaped less by direct self-interest than by two indirect ways in which pandemic policy gets linked to the general prevalence of zombie ideas in right-wing thought.

First, when you have a political movement almost entirely built around assertions than any expert can tell you are false, you have to cultivate an attitude of disdain toward expertise, one that spills over into everything. Once you dismiss people who look at evidence on the effects of tax cuts and the effects of greenhouse gas emissions, you’re already primed to dismiss people who look at evidence on disease transmission.

This also helps explain the centrality of science-hating religious conservatives to modern conservatism, which has played an important role in Trump’s failure to respond.

Second, conservatives do hold one true belief: namely, that there is a kind of halo effect around successful government policies. If public intervention can be effective in one area, they fear — probably rightly — that voters might look more favorably on government intervention in other areas. In principle, public health measures to limit the spread of coronavirus needn’t have much implication for the future of social programs like Medicaid. In practice, the first tends to increase support for the second.

As a result, the right often opposes government interventions even when they clearly serve the public good and have nothing to do with redistributing income, simply because they don’t want voters to see government doing anything well.

The bottom line is that as with so many things Trump, the awfulness of the man in the White House isn’t the whole story behind terrible policy. Yes, he’s ignorant, incompetent, vindictive and utterly lacking in empathy. But his failures on pandemic policy owe as much to the nature of the movement he serves as they do to his personal inadequacies.

Published in: on March 28, 2020 at 7:04 pm  Comments (1)  

Valerie Jablow researches the “philanthropists” who control education in DC

DCPS parent and blogger Valerie Jablow has been looking up facts and figures concerning education in DC for quite a while now. This longish post by her details who are the movers and shakers who control the schools.

The link is here.

Published in: on March 28, 2020 at 6:27 pm  Comments (1)  

Politics and disease: attacking both the messengers AND the doctors!

As a retired math teacher, I’ve played around a bit with some of the math models for pandemics. But since there is so much we don’t know, and the differential equations are not easy (especially since a lot of the variables are actually unknown) I have begun to realize how hard it is to predict the outcome of this world-wide outbreak. We need experts who have really studied this stuff for decades, not lying demagogues who attack those experts and those medical professionals.

This article is from WAPO today, March 28, 2020.

Coronavirus modelers factor in new public health risk: Accusations their work is a hoax

By William Wan and Aaron Blake

March 27 at 10:18 AM ET

Over the past two months, President Trump has regularly sought to downplay the coronavirus threat with a mix of facts and false statements.

In the one month since the first U.S. coronavirus death, America has become a country of uncertainty.

New cases of infection and casualties continue multiplying. New York and Louisiana hospitals are grappling with a flood of patients that threatens to overwhelm their health-care systems. Meanwhile, the president and political conservatives are increasingly agitating to end drastic restrictions meant to buy time and save lives.

Running beneath it all, in a continuous loop through our national psyche, are basic questions leaders are struggling to answer: When can we safely lift these quarantines? How many people could die if we do it too early? Just how dangerous will this pandemic turn out to be? And what exactly should be our next step?

This is why epidemiology exists. Its practitioners use math and scientific principles to understand disease, project its consequences, and figure out ways to survive and overcome it. Their models are not meant to be crystal balls predicting exact numbers or dates. They forecast how diseases will spread under different conditions. And their models allow policymakers to foresee challenges, understand trend lines and make the best decisions for the public good.

In recent days, a growing contingent of Trump supporters have pushed the narrative that health experts are part of a deep-state plot to hurt Trump’s reelection efforts by damaging the economy and keeping the United States shut down as long as possible. Trump himself pushed this idea in the early days of the outbreak, calling warnings on coronavirus a kind of “hoax” meant to undermine him.

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The notion is deeply troubling, leading health experts say, because what the country does next and how many people die depend largely on what evidence U.S. leaders and the public use to inform their decisions. Epidemiologists worry their research — intended to avert massive deaths in situations exactly like this pandemic — will be dismissed by federal leaders when it is needed most.

The peak

So much of the coming months and our country’s timeline depends on the peak of the coronavirus’s spread — its steepness, length and timing.

But here’s the thing about peaks: You often can’t tell where they are until you’re already past them, on your way down the other side.

And in a country as big as the United States, the peak will be not so much a single curve as it will the sum of many curves — as the outbreak spreads to different cities and regions at different times.

Nonetheless, a new model released Thursday by the University of Washington’s School of Medicine is one of the first to forecast a national peak. It projects that the peak in daily U.S. deaths will arrive in mid-April, and the tail end of that curve, subsiding below 10 daily deaths, will arrive by the first week of June.

But that projection comes with huge caveats because of estimations and assumptions that have to be built into the calculation, given how much is still unknown about the disease covid-19.

The model — created by the university’s Institute for Health Metrics and Evaluation — assumes, for example, that all remaining states that have not enacted strict restrictions on residents will do so in the next week once they see how grave the situation is in areas like New York.

But Florida Gov. Ron DeSantis (R) has refused to issue orders for people to stay at home. Alabama’s governor has similarly resisted. And this week, Mississippi’s governor issued an order defining almost all businesses as “essential” — including auto repair, bars and restaurants.

The Washington model assumes the entire country will maintain these strict restrictions until summer. But Trump has increasingly made clear he wants to reopen parts of the country by Easter on April 12. And on Thursday, Trump unveiled a plan to identify specific counties that he thinks should reopen soon.

The University of Washington model predicts that this first wave of infections will end by summer (with subsequent waves a possibility) and that the death toll during this initial period will range from 38,000 to 162,000 — a lower projection than some earlier models. But the actual death count in coming months will largely depend on how badly hospitals are overwhelmed and whether they receive supplies like ventilators that they desperately need.

On Thursday night, Trump cast doubt on experts’ projections on those as well. “I have a feeling that a lot of the numbers that are being said in some areas are just bigger than they’re going to be,” Trump told Fox News host Sean Hannity in a phone interview. “I don’t believe you need 40,000 or 30,000 ventilators. You know, you go into major hospitals, sometimes they’ll have two ventilators, and now all of a sudden they’re saying, ‘Can we order 30,000 ventilators?’”

On the attack

The attacks from Trump supporters against epidemiologists ratcheted up several bars on Thursday as pundits on the political right took aim at one of the world’s leading epidemiologists, Neil Ferguson of Imperial College in Britain.

Ferguson had co-written a paper this month estimating 510,000 deaths in England and 2.2 million in the United States — if those countries did not take drastic actions. The paper’s conclusions were so chilling that they launched leaders in both countries into action. The next day, Trump abruptly stopped encouraging Americans to go on with their lives and began urging them instead to work from home and not meet in groups of more than 10.

Since then, Trump has flipped back to wanting workers back at their jobs — framing it as a decision between saving the U.S. economy or a handful of lives. And his supporters have followed, attacking Ferguson online.

After Ferguson gave new testimony to British officials Wednesday, they hailed it as evidence that Ferguson and other experts were overselling the coronavirus threat. Fox News host Laura Ingraham wrongly stated that in his testimony Ferguson’s projection had been “corrected.” The chyron on her show Thursday night stated, “Faulty models may be skewing COVID-19 data.”

“Today — this is what our instinct was — the lead researcher did an about-face on those terrifying projections, the very projections that drove so much of our response,” Ingraham claimed on her show.

A Wall Street Journal columnist wrote that the revision “raises serious questions about the radical countermeasures inspired by public-health experts like Mr. Ferguson.”

Even one of Trump’s coronavirus task force coordinator, Deborah Birx, seemed to lean into the questioning of Ferguson. “I’m sure many of you saw the recent report out of the U.K. about them adjusting,” Birx said. “If you remember, that was the report that said there would be 500,000 deaths in the U.K. and 2.2 million deaths in the United States. They’ve adjusted that number in the U.K. to 20,000. So half a million to 20,000. We’re looking into this in great detail to understand that adjustment.”

But in fact, Ferguson had not revised his projections in his testimony, which he made clear in interviews and Twitter. His earlier study had made clear the estimate of 500,000 deaths in Britain and 2.2 million in the United States projected what could happen if both took absolutely no action against the coronavirus. The new estimate of 20,000 deaths in Britain was a projected result now that Britain had implemented strict restrictions, which this week came to include a full lockdown.

But the argument over models in some ways is beside the point, said Natalie Dean, a biostatistician at the University of Florida. “The models are planning tools, but it doesn’t take a genius to look at what’s happening in Italy and realize that we’re on the same trajectory,” said Dean, who is working on coronavirus vaccine evaluation with the World Health Organization. “That should be enough to tell us we need to be doing more in reaction.”

A warning from pandemics past

One clear warning from epidemiology of past pandemics is the danger of lifting restrictions — as Trump wants to do in two weeks — too soon.

A seminal 2007 paper shows what happened in several U.S. cities when they eased restrictions too soon during the 1918 flu pandemic. Those cities believed they were on the other side of the peak, and, like the United States today, had residents agitating about the economy and for relaxing restrictions.

Once they lifted them, however, the trajectory of those cities soon turned into a double-humped curve with two peaks instead of one.

This chart shows the double-humped peaks of deaths during the 1918 flu in St. Louis. The city imposed strict restrictions early on but loosened them under pressure from its citizens, only to see deaths jump again. (Courtesy of JAMA and Howard Markel)

Two peaks means you get the overwhelmed hospitals, the death and destruction, without that flattening benefit people were trying so hard to achieve with arduous restrictions.

“Knowing when to release the throttle is hard. There’s is no button that says push me now,” said Howard Markel, a historian and physician at the University of Michigan who co-wrote the 2007 paper along with a top CDC official, Martin Cetron. “But the trick is to be patient, not to jump the gun. Otherwise, all that happens is you get more cases, more deaths and everything you worked so hard for with those restrictions just goes to waste.”

One of the perpetual frustrations of trying to prevent disease rather than curing it is that it’s often difficult for the public to appreciate the disasters you help them avoid.

“The problem is there’s no metric for prevention. How many cases you avoid. How many lives you save,” Markel said. “That’s why it’s so hard to stay the course but so important, too.”

But one factor many modelers failed to predict was how politicized their work would become in the era of President Trump, and how that in turn could affect their models.

Published in: on March 28, 2020 at 1:29 pm  Leave a Comment  

Concerns about Mathematical Models of Pandemics

This is from Science, journal of AAAS.

With COVID-19, modeling takes on life and death importance

• Martin Enserink, Kai Kupferschmidt

See all authors and affiliations

Science  27 Mar 2020:

Vol. 367, Issue 6485, pp. 1414-1415

Dutch models of COVID-19 are designed to help prevent overloading of hospitals and the need to transfer patients.

Jacco Wallinga’s computer simulations are about to face a high-stakes reality check. Wallinga is a mathematician and the chief epidemic modeler at the National Institute for Public Health and the Environment (RIVM), which is advising the Dutch government on what actions, such as closing schools and businesses, will help control the spread of the novel coronavirus in the country.

The Netherlands has so far chosen a softer set of measures than most Western European countries; it was late to close its schools and restaurants and hasn’t ordered a full lockdown. In a 17 March speech, Prime Minister Mark Rutte rejected “working endlessly to contain the virus” and “shutting down the country completely.” Instead, he opted for “controlled spread” of the virus while making sure the health system isn’t swamped with COVID-19 patients. He called on the public to respect RIVM’s expertise on how to thread that needle. Wallinga’s models predict that the number of infected people needing hospitalization, his most important metric, will taper off next week. But if the models are wrong, the demand for intensive care beds could outstrip supply, as it has, tragically, in Italy and Spain.

COVID-19 isn’t the first infectious disease scientists have modeled—Ebola and Zika are recent examples—but never has so much depended on their work. Entire cities and countries have been locked down based on hastily done forecasts that often haven’t been peer reviewed. “It’s a huge responsibility,” says epidemiologist Caitlin Rivers of the Johns Hopkins University Center for Health Security, who co-authored a report about the future of outbreak modeling in the United States that her center released this week.

Just how influential those models are became apparent over the past 2 weeks in the United Kingdom. Based partly on modeling work by a group at Imperial College London, the U.K. government at first implemented fewer measures than many other countries—not unlike the strategy the Netherlands is pursuing. Citywide lockdowns and school closures, as China initially mandated, “would result in a large second epidemic once measures were lifted,” a group of modelers that advises the government concluded in a statement. Less severe controls would still reduce the epidemic’s peak and make any rebound less severe, they predicted.

But on 16 March, the Imperial College group published a dramatically revised model that concluded—based on fresh data from the United Kingdom and Italy—that even a reduced peak would fill twice as many intensive care beds as estimated previously, overwhelming capacity. The only choice, they concluded, was to go all out on control measures. At best, strict measures might be periodically eased for short periods, the group said (see graphic, below). The U.K. government shifted course within days and announced a strict lockdown.

It’s not that the science behind epidemic modeling is controversial. Wallinga uses a well-established model that divides the Dutch population into four groups, or compartments in the field’s lingo: healthy, sick, recovered, or dead. Equations determine how many people move between compartments as weeks and months pass.

“The mathematical side is pretty textbook,” he says. But model outcomes vary widely depending on the characteristics of a pathogen and the affected population.

Because the virus that causes COVID-19 is new, modelers need estimates for key model parameters. Wallinga is now confident that the number of new infections caused by each infected person when no control measures are taken—which epidemiologists call R0—is just over two. And he trusts data showing that 3 to 6 days elapse between the moment someone is infected and the time they start to infect others.

From a 2017 survey of the Dutch population, the RIVM team also has good estimates of how many contacts people of different ages have at home, school, work, and during leisure. Wallinga says he’s least confident about the susceptibility of each age group to infection and the rate at which people of various ages transmit the virus.

Compartment models assume the population is homogeneously mixed, a reasonable assumption for a small country like the Netherlands. Other modeling groups don’t use compartments but simulate the day-to-day interactions of millions of individuals. Such models are better able to depict heterogeneous countries, such as the United States, or all of Europe. The World Health Organization organizes regular calls for COVID-19 modelers to compare strategies and outcomes, Wallinga says: “That’s a huge help in reducing discrepancies between the models that policymakers find difficult to handle.”

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In their review of U.S. outbreak modeling, Rivers and her colleagues note that most of the key players are academics with little role in policy. They don’t typically “participate in the decision-making processes … they sort of pivot into a new world when an emergency hits,” she says. Rivers argues for the creation of a National Infectious Disease Forecasting Center, akin to the National Weather Service. It would be the primary source of models in a crisis and strengthen outbreak science in “peacetime.”

Policymakers have relied too heavily on COVID-19 models, says Devi Sridhar, a global health expert at the University of Edinburgh. “I’m not really sure whether the theoretical models will play out in real life.” And it’s dangerous for politicians to trust models that claim to show how a littlestudied virus can be kept in check, says Harvard University epidemiologist William Hanage. “It’s like, you’ve decided you’ve got to ride a tiger,” he says, “except you don’t know where the tiger is, how big it is, or how many tigers there actually are.”

Models are at their most useful when they identify something that is not obvious, says Adam Kucharski, a modeler at the London School of Hygiene & Tropical Medicine. One valuable function, he says, was to flag that temperature screening at airports will miss most coronavirus-infected people.

There’s also a lot that models don’t capture. They cannot anticipate, say, an effective antiviral that reduces the need for hospital beds. Nor do most models factor in the anguish of social distancing, or whether the public obeys orders to stay home. In Hong Kong and Singapore, “It’s 2 months already [of such measures], and people are really getting very tired,” says University of Hong Kong modeler Gabriel Leung. Recent data suggest the virus may be spreading faster again in both cities, putting them on the brink of a major outbreak, he adds.

Long lockdowns to slow a disease have catastrophic economic impacts and may devastate public health themselves. “It’s a three-way tussle,” Leung says, “between protecting health, protecting the economy, and protecting people’s well-being and emotional health.”

The economic fallout isn’t something epidemic models address, says Ira Longini, a modeler at the University of Florida—but that may have to change. “We should probably hook up with some economic modelers and try to factor that in,” he says

Published in: on March 26, 2020 at 9:01 pm  Leave a Comment  
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