Guest Post by Kevin Kilty
No planning is likely possible without calculations of what the future may hold, but such calculations are fraught with uncertainty when they also involve exponential processes. Indeed, as the author of one chapter in a recent book [1] states:
“One characteristic of an exponential growth process that humans find it really difficult to comprehend is how fast such a process actually is. Our daily experiences do not prepare us to judge such a process accurately, or to make sensible predictions.” [emphasis is mine.]
Quests to reveal a future governed by exponential processes, or what people guess to be exponential processes, run through many themes here at WUWT — future climate, energy demand, economics, epidemics. This guest contribution takes a selected look at exponential growth. Two examples are historical, and perhaps obscure, but pertinent. The third one, which comprises the bulk of this essay, is an examination of R0, which dominates the present imagination.
Failure on the Plains
Cattle arrived on the Northern Plains of the U.S. frontier first in the mid-1860s. The industry was infested with promoters, people with interests in railroads and such, who promoted using tales of how to get rich on the plains to Eastern and European investors. Some early investors made money selling to bigger cattle corporations. But the industry was based on cattle herds rather than titles to real property, and cattle counts were notoriously difficult to carry out. Thus, much of the promotion and accounting became based on “book” counts. These were not credible, but had the effect of a stampede to the plains financed by people who little understood the business or its risks.
Figure 1 shows an actual book count against a Fibonacci series representing a hypothetical rabbits.[2] The exponential behavior of the book count is obvious.
Figure 1.
The hard winter of 1886-1887, which was an instance of weather not climate change, wiped out many live cattle, but it wiped out many larger book counts. It provided an opportunity for the range managers to adjust plainly inaccurate inventories and save face at the same time. The story at the present day, for the few who know anything of the story at all, is of millions of cattle perishing in blizzards. It is much more acceptable to be bankrupted by weather than by foolish belief in an exponent.
Is there a modern equivalent? Well, the strangely smooth curve of Chinese deaths from COVID19 looks like one. It resembles a calculated curve with a certain goal in mind, rather than a measured curve with all the wiggles back and forth like the comparison curves from other countries.
Projection of Electric Energy Demand
Electric energy demand grew at an exponential rate after WWII, especially during the 1960s, when the grid expanded into every conceivable corner of North America, and new uses, such as the mercury vapor light, expanded into every conceivable market. The near perfect fit of geometrical growth of 7.13% per annum to electrical demand in 1960-1972 as Figure 2 shows, led to wild predictions of future demand and its consequences. A simple projection of constant geometrical growth (Figure 3) arrives at a staggering demand of 12 TWhr in year 2000, and one might be tempted to dismiss it. However, 1972 a workshop held at Cornell, sponsored by NSF, produced a “consensus” estimate of 10.25 TWhr, which is not much lower. [3] These estimates were driven by exponential growth in usage and population.
Figure 2.
What occurred in the 1970s was a constant drumbeat of future shortages, the decimation of free flowing rivers, the needed changes to society and the economy, the need for government mandates because government is the only institution big enough to deal with the crisis. Untold amounts of taxpayer and private money poured into schemes long forgotten (magnetohydrodynamics) or schemes that should have been (geothermal). The crisis prompted everyone to push their preferred hobby horse. Sounds familiar.
Figure 3.
What actually happened post 1970s? Actual electrical energy consumption never reached 40% of these projections. Figure 4 shows electric consumption to the present time along with the supply available from selected sources. Note the supply from petroleum. It provided a large source of electrical energy pre-1973. However, the two oil price shocks (1973 and 1979) had the effect of immediately putting a halt to the growing use of petroleum to generate electricity and diminished it each time.[4] People may not comprehend the speed of exponentials, but they respond quickly to prices.
More interesting still is that not only did demand not grow exponentially after 1972, but that post 2008 it hasn’t grown at all, as Figure 4 also shows. We appear to have reached a point where slowing economic growth has enabled innovation such as outsourcing, container ships, LED light bulbs and myriad other things to provide increased standard of living without use of more energy. Can it continue? Time will tell.
Figure 4.
Trajectory of a Pandemic
In times of crisis, real or imagined, people become fixated on certain technical measures or parameters of the problem, which become something like fetishes. The mean temperature of the Earth, the level of CO2, or its rate of production all play such a role in climate change. The parameter R0, the basic reproductive ratio, plays such a role in the present COVID19 crisis. Let’s explain what R0 describes, and what it has to do with some selected observations about the present pandemic.
What is R0?
The best way to explain R0 is through a simple model of an epidemic involving three populations: X, the population of people who are susceptible to a disease but who are presently not infected; Y, the population of infected (and infectious) people; and Z, the population who have recovered, and are not for the present time likely to fall back into population Y.
Many factors affect population X — births, deaths, migration, and so forth. However, over a short period of an epidemic we might consider only becoming infected and transitioning to population Y as having any pertinence. People often model the factor describing this transition as a term like -BXY. The product of populations (XY) indicates something about the probability of an X person encountering an infected one; B is a factor of transmissibility describing the probability that the encounter between an X and a Y results in X becoming infected.
It should be obvious that in the short term any person leaving the group of Xs does so by entering the Ys. So, the equation describing the rate of change of Y contains the term +BXY. However, the change of Y also depends on the rate at which the infected become well, and transition to the group of Zs — a rate we call U, and the rate at which infected people die and vanish from the model altogether — a rate we call V. Thus our differential equation for Y is
dY/dt = (BX – (U+V)) Y
Someone familiar with differential equations will recognize the factor (BX – (U+V)) as a sort of time constant; large BX tends to make this time constant positive, and results in a population of Y which grows exponentially; large (U+V) tends to push it toward negative values which would result in exponential decay.
People don’t like to deal with summations of factors in a time constant, and in the case of epidemics what people have done is to turn the time constant into a ratio, with those factors tending to make it positive in the numerator and those making it negative in the denominator.
The resulting definition is something like R0 = BX/(U+V) ref.[5]
There is a tendency, apparently even among the medical community, to think of R0 as a sort of time constant, but it is not. It is a dimensionless measure more akin to what engineers would call a figure of merit. There is also a tendency to think of it as intrinsically a function of the disease itself. It is not. Let’s discuss each factor in turn and explain what about each factor is important to the epidemic.
The factor B has to do not only with how easily a disease intrinsically jumps from person to person (like measles with a large value of B), but also has to do with cultural and social factors of the Xs. Touchy-feely sorts of societies will make B larger and push R0 to a value larger than 1.0; other societies have more intrinsic distance and push B toward smaller values. All sorts of strategies to increase social distance — lockdowns, isolation of the vulnerable, isolation of the infected and even disinfecting surfaces — seek to make B smaller in value.
X, the population of unaffected people, doesn’t necessarily include the entire population. There are people with intrinsic immunity to the disease. For example, Willis’s contribution from some time ago pointed out that on the Grand Princess not everyone who was exposed became infected. Perhaps only 20-40% did.[6] Obviously X depends on the age distribution and also on the distribution of other morbidities in a population. A common strategy to reduce X is immunization.
Factor U has to do with the virulence of the disease, but also has to do with population characteristics such as age distribution and other morbidities. Within my home state we have an unusually large fraction of the known infected who have recovered quickly. It suggests a lower R0 than places displaying long convalescent periods. Does this tell us anything valuable about COVID19, or does it simply reflect differences in various state departments of health making assessments of recovery? One strategy toward boosting U is to employ treatments such as what New York City is attempting with chloroquine.
What is important about R0?
R0 is not a constant. As a disease progresses through a population X becomes smaller and tends to push R0 to smaller values. Eventually it becomes small enough that R0 falls to a value less than one and the epidemic peters out. This is the principal factor that converts the initial exponential growth of an epidemic to a logistic sort of curve toward its conclusion. Also, just like example about energy, people change their behavior in a time of stress. They avoid other people, and improve hygiene — factors which improve B. Also, different ethnic groups and different parts of the U.S. will display different values of R0. These combined factors probably explain the wiggly behavior of the various graphs on the Daily Coronavirus Graph page.
Getting a handle on R0
Having an accurate estimate of R0, especially early in an epidemic cycle, would be very useful for public health policies. Here are the hurdles one has to clear to get an accurate value:
First, the most valuable estimate of R0 to get ahead of an epidemic is one made early in the epidemic. Without experience to draw upon a person has to use observations. The only population leading to a useful estimate of R0 is the infected, Y. We have no idea how this population is growing at present relative to X.
Second, I have commented elsewhere about individuals local to me who are not only included in the “cases” of two neighboring states (double counted), but who may have been placed within the data at the wrong time of exposure and infection. Early estimates of R0 are made when there are very few infected individuals. Such estimates are very sensitive to errors of observation. Observations placed erroneously too far along in the epidemic will have the effect of erroneously making R0 too large; while those placed erroneously too early will make R0 appear, erroneously, too small.
Because all of the factors involved in R0 keep changing with time, one has to keep collecting timely data for evaluation about effectiveness of strategies. Thus one is always presented with the problem of limited individuals who are pertinent, and then decisions about which individuals should be counted, and exactly where to place them in sequence. At no time does estimating R0 become simple.
Third, because R0 is not a time constant, but rather a dimensionless figure of merit, the pertinent observations for its estimate are of the growth generation to generation — that is, growth of Y in the chain of transmission from person to person. In my state public health officials estimate that more than 60% of the infected can explain where they were infected. However, this estimate has to be tempered with knowledge of how faulty people’s memories are.
One MD has spoken elsewhere about observations, such as the spread through the call center at Daegu, South Korea, which suggest an R0 well below 1.0. However much his number may pertain to the special case of this particular call center, the value of R0 cannot be below 1.0 generally. If it were, the plainly obvious growing epidemic across the U.S. at present would require an utterly improbable set of initial conditions.
Similarly, the large values of R0 (2.0 to 2.6) used by Neil Ferguson, along with estimates of generation duration and other parameters, propelled initial panic. One can tell from the press conferences that Dr. Fauci, Trump’s principal advisor, is still highly influenced by these early estimates.These were guesses, albeit educated ones. Apparently Ferguson is stepping back from these initial estimates. This is just my opinion, but it appears that we, across the Western world, were unprepared to gather the sort of data early to make valuable estimates of R0 at an actionable time — for example rather than daily counts of infections we need counts by generation of spread, and estimates of uncertainty. Estimates of deaths in Britain from 20,000 to 500,000 do nothing to aid in policy prescriptions.
Conclusion
There is no doubt that we will survive this pandemic, but at great cost. A famous quotation seems apropo:
“ If we are victorious in one more battle with the Romans, we shall be utterly ruined.”
Phyrric, 275 B.C.
After this crisis has passed we really need to have a sober evaluation of strategies versus outcome, and decide whether we might have done better. We should decide whether our goals were even sensible. Nic Lewis’s contribution is an example of sober analysis; so is Alec Rawls’s. We do not need a second such victory over exponents.
Notes:
[1] Philip Dutre, Thinking and Conscious Machines?, in “A Truly Golden Handbook”, Ed. by Veerle Achten, Geert Bouckaert, Erik Schokkaert, Leuven University Press, 2017.
[2] Dan Fulton, Failure on the Plains, Big Sky Books, Montana State University Press, 1982.
Throughout Fulton’s early chapters quotations refer to the book counts as “arithmetic progressions” when in fact they are geometrical. The book count data came from Robert Strahorn, one time superintendent of the Union Pacific Railroad.
[3] This projection, along with the projections of the Federal Power Commission and National Petroleum Council would be featured in Congressional testimony in May 1972 and in a companion paper in (Chapman, et. al., Science, v.78,p.703-708,1972) as Table 1. While the authors stated that these projections might prove too high, they emphasized that “…to the extent that past population growth rates continue, the projections of Table 1 are supported…”
[4] All electrical consumption data are from EIA spreadsheets.
[5] Martin Nowak, Evolutionary Dynamics, Belknap/Harvard Press, 2006. Nowak’s definition is not exactly like mine but is functionally the same.
[6] https://wattsupwiththat.com/2020/03/16/diamond-princess-mysteries/
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“Third, because R0 is not a time constant, but rather a dimensionless figure of merit, the pertinent observations for its estimate are of the growth generation to generation — that is, growth of Y in the chain of transmission from person to person. In my state public health officials estimate that more than 60% of the infected can explain where they were infected. …”
I heard some commentary today on the radio about how puzzling it is that California hasn’t been impacted nearly to the degree that New York has been (so far). California should be severely impacted based on its demographics and its ties to Asia the commentator pointed out. Is it the current weather? Is it the climate? Is it the culture and society customs there?
One possibility may be is that Californians for the most part are not reliant upon public transit. People in the west generally rely on private transportation in privately owned fossil fueled automobiles and often drive solo in isolation.
I understand that there are many strains (8 or more) of this virus, and that California’s seed appears to have come from Washington state, while New York’s apparently straight from China. It may have something to do with it; however, the difference in Eastern/Western lifestyles may play a large role.
I agree with you regarding and our loss of freedoms. It makes no sense that I can’t go sit by the ocean by myself. Can’t walk on nature trail, by myself. Can’t go fishing, by myself.
I’m currently (re) reading “1984” — going through my library to find material to keep me busy — and so many parallels to what is happening today, it is really disconcerting. Brilliant book though.
Hey Kevin,
Decent piece of writing though I don’t quite get a main message of your text – are you saying that fears are grossly exaggerated and cost of ‘mitigation policies’ may be actually higher than cost of epidemic itself?
No, I am saying that prediction with exponentials is fraught with uncertainty, has often been very inaccurate, and that being so, perhaps our decisions should take into account other concerns and a much bigger view of human affairs.
The Wuhan deaths model I developed in a comment yesterday to the physicians letter post is still working quite well today for NY (98.3% accurate), Florida (102%) , and US total (97.7%) based on reported cases. It fails (large underestimates) for Italy, France, and Spain because of overwhelmed health systems. It also off for UK (another underestimate), dunno why.
Rud, I liked the model but I can’t find where it was to refer back to it. Wasn’t is “tuned” to US data initially. I would be surprised if there is enough similarity with testing and reporting in other countries for this to be portable.
” It also off for UK (another underestimate), dunno why.”
Probably because the UK data collection is a totally unstructured, anarchic mess and is likely being tailored before being released. Zero transparency. Reporting methods are probably evolving in time in many regions, making the dataset totally heterogeneous.
I don’t think UK case data is even worth plotting. Deaths may be more reliable though likely contaminated by flu cases due to lack of testing equipment.
Something to consider is that natural social distancing if a function of population density. That is, as population density goes down, people have less frequent and less close contact, acting effectively in the same manner as purposeful isolation. Another way of putting it is that, in rural areas, the effects of COVID-19 were observed later and are progressing more slowly than in NYC, and New Orleans. Both the initial R0 value, and change in time, are smaller in rural areas than in urban areas. This is a pandemic exacerbated by urban environments and lifestyle (clubbing, concerts, sporting events, and public transportation). It is a consequence of urban living and it is no coincidence that it first appeared in China, which has created the largest mass migration of people in history, moving them from rural areas to urban areas. It hasn’t helped that the migration took place so rapidly that the cultural norms didn’t have a chance to evolve (e.g. outdoor wet-markets). Interruption of the economy may become a way of life for the world if we don’t find another way to deal with future pandemics other than ‘sheltering in place.’
Salute!
TNX, Clyde.
When the dust settles and 99.99% of the corona critters fall to the floor or dirt to die, we should hope to see some data on the “R0” and other stats compared to the rural and urban populations densities as well as cultures.
And BTW, I feel NOLA will come out better than NYC. You do not have hundreds of thousands living in huge apartment complexes. You do not have mass transit on the scale of Manhattan or even Boston or Chicago. OTOH, the Big Easy is very “social”. I grew up there and can provide much “anti-total” testimony, heh heh.
Gums sends…
Millions of young people like yourselves will suffer because of this HUMAN stupidiy this is just a normal cold flu virus that will not affect warm countries but your leaders and scientists are incredibly stupid today so you will suffer beleive me I know I was a scientist there in Australia in the 90,s and they were incredibly stupid However in the 50s they were the smartest scientists in the world its a pity. Trumps stupidity has produced 53 milliom unemployed people for a nothing burger. Trump needs to get rids of swamp materials such as Fauci who predicted that everybody would die from HIV
Eliza
I’m not surprised to read that you are no longer a scientist.
200000 old peolple die every day wake up USA. This is normal death rate Trump is finished as being very stupid
NOT normal – younger man, 38, on pathway to corona-virus death:
“I was struggling to breathe. I felt like I was slowly drowning and I was sitting there thinking I’m not going to make it until midnight,” he said. Santilli says the antimalaria drug Hydroxychloroquine and Azithromycin brought him back to life. The 38-year old Detroit resident was prescribed the drugs a little more than a week ago at Henry Ford Macomb where he was hospitalized for COVID-19.
He says a doctor told him they’d exhausted treatment options. An infectious disease physician recommended he try both. “He stated at that point for COVID-19 patients they saw a lot of positive results in China and South Korea it would be advantageous to try it,” Santilli said. “Right away I saw improvements in a few hours: the gasping for air stopped; a lot of my symptoms went away, and really it was a turning point almost a 180 degree turn as to what I was experiencing.”
https://techstartups.com/2020/03/31/jim-santilli-a-coronavirus-patient-says-hydroxychloroquine-and-azithromycin-saved-his-life/
Hi _Jim, – The detail I’ve read is the chloroquine based drugs are effective when administered early in Wuhan virus infection. And not showing great results in cases where the virus has had more unopposed time. Of course in different people there is variability of their immunological activity.
re: “The detail I’ve read is the chloroquine based drugs are effective when administered early …”
Yeah, been “all over” that in other, previous threads … see:
https://techstartups.com/2020/03/30/hydroxychloroquine-azithromycin-z-pak-continue-show-positive-results-coronavirus-patients/
https://techstartups.com/2020/03/30/dr-william-grace-thanks-hydroxychloroquine-not-death-hospital/
https://townhall.com/columnists/kevinmccullough/2020/03/29/hydroxychloroquine-help-is-on-the-way-n2565926
The BIG French study (wordy and technical): https://www.mediterranee-infection.com/wp-content/uploads/2020/03/COVID-IHU-2-1.pdf
Something people could do early when symptoms first show without needing a doctor’s prescription is use a natural zinc ionophore, like quercetin and Epigallocatechin-gallate (EGCG), and zinc. All available at Amazon.
Zinc ionophore activity of quercetin and epigallocatechin-gallate: from Hepa 1-6 cells to a liposome model
https://www.ncbi.nlm.nih.gov/pubmed/25050823
Very encouraging, there should be thousands of such anecdotes by now. Where are they?
You’re right, it’s not normal. That’s why prudent people ask “What are the co-factors?” Does he vape? Smoke? Take hypertension meds? Diabetic?
Trump has no choice. He has to play the long game.
We are still looking back when we are discuss the virus.
What should we have done?
…And we are comparing country to country with the assumption we can get back to the world we knew before the virus.
The covid virus has killed world tourism and it appears world tourism will be dead for years.
New York city will loss let say a million tourism jobs and tourism sustained jobs over the next few months…
and World tourism is dead until there is:
1) Two year from now, Vaccine is developed and is used in all developed country
We may have lost this option. There is now virus spread in Africa, India, Pakistan, and so on. It is likely there will be multiple strains of the virus. Current vaccines are only effective for one strain. A two week incubation period for the virus makes mass world travelling not likely if there are multiple strains of the virus.
2) Three years from now. An effective universal vaccine to all covid virus is developed, tested, and distributed worldwide.
https://www.statista.com/topics/962/global-tourism/
Globally, travel and tourism directly contributed approximately 2.9 trillion U.S. dollars to GDP in 2019. In the same year, the United States’ travel and tourism industry directly contributed the highest amount to global GDP, with a total of 580.7 billion U.S. dollars. Meanwhile, the city and special administrative region of Macau generated the highest share of GDP through direct travel and tourism of any economy worldwide.
Read more
Bill Powers,
What you have rightly noted applies to the UK, also.
And here, our Secretary of State for Transport has started to talk about pushing the populace onto Public Transport.
Now Public Transport has its place – I commuted into London for almost a quarter of a century, using public transport.
But no car – no (real) freedom.
BBC report of Grant Shapps’ announcement [slipped out under Covid-19 cover] is now hard to find.
Beware.
Auto
“innovation such as outsourcing”
Underpaid workers with no unions allowed, no safety protection, and zero pollution control on plants is “innovation” now?
Three strikes in a row … and the ump says “You’re out!”
(NLRB, OSHA and EPA involved respectively; I can’t help but add: You really are a moron.)
What the hell are you trying to say?
re: “What the hell are you trying to say?”
You are an idiot. I just took a more diplomatic way of saying it the first time …
“…and cattle counts were notoriously difficult to carry out.”
Not at all. You just count the legs and divide by four.
Try estimating the size of a herd of humans. You only have to divide by two but it’s not so easy.
I don’t have mathematical modelling expertise but I can use logic to see if the assumptions and inputs made by modellers are correct. Here is the kind of argument I have been making on another forum:
From the Wall St Journal:
Is the Coronavirus as Deadly as They Say?
Current estimates about the Covid-19 fatality rate may be too high by orders of magnitude.
By Eran Bendavid and Jay Bhattacharya. Dr. Bendavid and Dr. Bhattacharya are professors of medicine at Stanford.
“Fear of Covid-19 is based on its high estimated case fatality rate — 2% to 4% of people with confirmed Covid-19 have died, according to the World Health Organization and others. So if 100 million Americans ultimately get the disease, two million to four million could die. We believe that estimate is deeply flawed. The true fatality rate is the portion of those infected who die, not the deaths from identified positive cases.
The latter rate is misleading because of selection bias in testing. The degree of bias is uncertain because available data are limited. But it could make the difference between an epidemic that kills 20,000 and one that kills two million. If the number of actual infections is much larger than the number of cases — orders of magnitude larger — then the true fatality rate is much lower as well. That’s not only plausible but likely based on what we know so far…
“…the real fatality rate could in fact be closer to 0.06%…
“…First, the test used to identify cases doesn’t catch people who were infected and recovered. Second, testing rates were woefully low for a long time and typically reserved for the severely ill. Together, these facts imply that the confirmed cases are likely orders of magnitude less than the true number of infections. Epidemiological modelers haven’t adequately adapted their estimates to account for these factors…
“…An epidemic seed on Jan. 1 implies that by March 9 about six million people in the U.S. would have been infected. As of March 23, according to the Centers for Disease Control and Prevention, there were 499 Covid-19 deaths in the U.S. If our surmise of six million cases is accurate, that’s a mortality rate of 0.01%, assuming a two week lag between infection and death. This is one-tenth of the flu mortality rate of 0.1%…”
Furthermore, the numbers (as opposed to the shape of the curve) will be strongly affected by risk co-factors such as those of Northern Italy:
Population density
Local air pollution
Population age / demographics
Local sanitation levels
Type, age and condition of housing
Forms of heating / cooling / ventilation and the consequent indoor environments (heat pumps good, coal fireplaces bad)
Rates of smoking
Flows of international travellers from epicentres of contagion
Misguided “anti-xenophobia” virtue-signalling over exotic communities that are gateways for infection (New York encouraged people to attend a Chinatown festival in mid February to display their anti-xenophobic virtue).
New York “City” will be an epicentre because of some of the the above factors. the urban-area low density suburban sprawl will not be affected as much; nor will most of the urban areas marked by low-density sprawl without the dense centre like NYC has. Northern Italy is uniquely affected by all factors. Other parts of Italy are only affected at a fraction of the level as yet.
If the true rates of infection in the early stages are far higher than the rates of people who actually get sufficiently ill to get tested, this means the contagion is far less deadly that the “deaths divided by confirmed cases”. The exponential nature of infection means that for all the confirmed cases, there must be orders-of-magnitude more asymptomatic or mild-illness infections out there.
Unfortunately a random “representative subset” test for the virus itself, to inform us about likely “total rates of infection”, needed to be done a long time ago. Potentially there will now be a lot of people who would test negative for the virus, who were in fact infected already and recovered or did not get ill, or not seriously. The exponential rate of spread of “unknown infections” means that “herd immunity” will arrive a lot earlier than guessed, at the epicentres.
The article in the Wall Street Journal by two well credentialled experts is correct to base its conclusions on early “representative subset” testing. It is very unfortunate that there are so few examples of this testing. Next pandemic, perhaps? Now all we can do is wait for an antibodies test.
Another potential cause for optimism is the possibility that previously-circulating coronaviruses confer some degree of immunity to COVID-19.
Of course we should lock down epicentres, and close down sports stadiums, megachurches, carnivals, etc. The more we know, the more we can do targeted mitigation instead of universal lockdowns. Sometimes medical experts have to defer to economics experts, otherwise all sorts of things that kill a few people, but provide for modern economic productivity, would be banned. The spectrum of potential economic breakdowns does include: total collapse of the monetary system of exchange; collapse of the supply chain for essentials; mass social breakdown. The only pandemic worth this would be one that was going to kill us all anyway.
“Estimating the optimal lockdown time”
Links at
http://catallaxyfiles.com/2020/04/01/estimating-the-optimal-lockdown-time/
Big News.
China will start to make public the number of asymptomatic cases
http://www.bjnews.com.cn/opinion/2020/03/31/711499.html
As most informed china followers know the cases reported have not generally included asymptomatics.
That will change
http://www.bjnews.com.cn/opinion/2020/03/31/711499.html
‘Some data also suggest that the infectious problems of asymptomatic infections cannot be underestimated. Researchers from Ningbo Centers for Disease Control and Prevention published a paper recently that analyzed the epidemiological characteristics of 157 locally diagnosed patients and 30 asymptomatic infections and found that the infection rate of the close contacts of the former was 6.3%, and the latter was 4.11%. This is widely interpreted as the difference in infectivity between asymptomatic infections and confirmed cases.”
“For all places, these measures should be allowed to land without any discount. On the one hand, localities must not conceal confirmed cases for “zero additions.” Tracing the source of confirmed cases is an important way to find asymptomatic infections. The most worrying situation of the epidemiological investigation is “unknown sources”. Only open and transparent, “deep-informed” information reports can accurately characterize the virus’s transmission path, thereby allowing “invisible people” to appear.
On the other hand, it is necessary to increase active screening. Although asymptomatic infections may sound difficult to prevent and control at first glance, the concealment of transmission, subjectivity of symptoms, and the limitations of discovery will indeed increase the difficulty of prevention and control, but they cannot escape the law of virus transmission. Screen close contacts, key areas, and key populations of cases that have been found and those with asymptomatic infection.”
Nothing that comes out of China is worth a damn.
There are videos circulating showing the virus being intentionally spread by infected persons, mostly Chinese, intentionally spitting on elevator buttons, sneezing on food in markets, etc. This seems to have taken place in many countries, including China. Fake?
Doesn’t seem so. There are many stories of this out there. What would motivate one to do this?
Standing on the stage being payed for it.
I meant official announcements by the CCP. Even what doctors say is suspect because everything is controlled.
Steven, very interesting information. Do you know whether there is a difference in fatality rate for infections by asymptomatic people?
have not seen anything.
did see this. interesting data on sauna?
https://www.youtube.com/watch?v=EFRwnhfWXxo
I heard about the stimulus by alternating warm/cold. And in general the function of fever (attacking invaders) is well known. It seems logic to combine ‘warming’ with ‘cooling’.
The numbers given for the Spanish flu look very comparable with the present virus: 20% of cases become hospitalized with pneumonia (in the army camps), half of the people with pneumonia dies.
Unfortunately if test data that reveals percentage of asymptomatic cases is to be of use, it needed to have been done very early in the outbreak. Otherwise, tests done later will miss everyone who has already thrown off the virus. The Wall Street Journal article I quoted above, uses the one good example of westerners evacuated from Wuhan, to extrapolate likely estimates of asymptomatic incidence. Given that infection proceeds exponentially, this could mean orders of magnitude more people affected and asymptomatic, than “confirmed infections” in people tested because of symptoms.
“The hard winter of 1886-1887, which was an instance of weather not climate change,”
Sure it was. With all those cows producing all that methane, it’s no wonder the climate warmed … er .. I mean changed and destabilised.
“The covid virus has killed world tourism and it appears world tourism will be dead for years”
The best news I have heard over last days! We will get our country and roads back.
M
Kevin and others, you may find my simulation of the COVID-19 epidemic interesting. I also noted that while an R0 of 2.6 may have been true initially, it can’t be true anymore the minute the population becomes aware and begins to take precautions. In this small example, I try to find the suppression level that will be sustainable with existing capacity. Lots of assumptions involved, but it is a surprisingly low level of suppression that can meet the goal. To stop it entirely requires much more serious intervention:
https://naturalclimate.wordpress.com/2020/03/24/coronavirus-model-what-level-of-suppression-is-enough/
In summary, the total incidence of COVID-19 illness over the next five years will depend
critically upon whether or not it enters into regular circulation after the initial pandemic wave,
which in turn depends primarily upon the duration of immunity that SARS-CoV-2 infection
imparts. The intensity and timing of pandemic and post-pandemic outbreaks will depend on the
time of year when widespread SARS-CoV-2 infection becomes established and, to a lesser
degree, upon the magnitude of seasonal variation in transmissibility and the level of crossimmunity that exists between the betacoronaviruses. Longitudinal serological studies are
urgently required to determine the duration of immunity to SARS-CoV-2, and epidemiological
surveillance should be maintained in the coming years to anticipate the possibility of
resurgence.
https://www.medrxiv.org/content/10.1101/2020.03.04.20031112v1.full.pdf
The death is rising daily, but i am shocked how the chinese people survive that or that is just a plan to hide the news by the communist party.
hopefully waiting for the vaccine. cant see the rising of sudden death daily.
there can be a major problem in the whole world. It can bring a big crisis
Last week this time I’d never heard of R0, so take this for what it’s worth, but I think that in the way you seemed to mean it your statement that “R0 is not a constant” wouldn’t be considered exactly right in some circles.
My view is that in such circles R0 is instead thought of as the initial value of a variable R, which is the quantity that declines as the population acquires immunity. That is, although for a given disease R0 could change as human behavior does, it doesn’t change with immunity acquisition; that’s what R does. Viewed in this light, for a given initially susceptible population there would be a theoretical one-to-one relationship between any R0 > 1 and the resultant proportion of the initially susceptible population that ultimately gets infected.
Incidentally, you’re no doubt aware that the model you used is called the “SIR” (Susceptible-Infected-Recovered) model, where your X, Y, and Z populations are often called S, I, and R, respectively. To incorporate an incubation period, that model is sometimes expanded to an “SEIR” model, where E becomes those who are exposed but not yet infectious.
I have reservations about both, because they tacitly assume exponential decay. If you assume a different decay profile you can get greatly increased infectiousness peaks for the same initial doubling period.
Good clarification. The other R is known as Rt (but I think of it as Re, for effective). I have found the same thing about the exponential assumptions. They are handy if you want to do some shortcut math, but with simulation, I can abandon all that and can include any distribution that matches the data I am seeing best. Some of them, especially the “shedding rate” is very steep up front and decays fast, and presents a different way to look at susceptibility. If shedding at high volume early, the potential during exposure is MUCH higher, but this typically goes to near zero by day 10, so even if shedding a huge virus load at that point, the amount that is viable is almost zero (probably damaged / broken by your immune system, but easily detectable). In this case, you’ll get a double whammy which will make the spread risk extremely high right after incubation (possibly as symptoms are just developing), but nearly zero a few days later. This will have the effect of shortening the entire event for the population, and making spread more like embers feeding a brush fire, with very fast, wave-like behavior. This also helps the effect of separation as the viable time is shorter and the embers burn out fast. That isn’t in my simulation yet, but it could explain why this is so hard to contain. It would be like virulence^2 for a short time.
Indeed.
Of course, this is a particularly good example of “All models are wrong, but some are useful.” We know our calculations are just speculation, but they’re useful in that they show how slight an assumption change can result in a large outcome change.
I’m trying not to forget that this modeling stuff is mostly just a way of giving the numerate a false sense of certainty. Still, it would be nice to know the average impulse responses for the “E” (exposed-but-not-yet-infectious) and “I” (currently infectious) populations. So it’s too bad we probably won’t see anything reliable about that.
When you use the term “load” it prompts this question.
Is there a critical load of infectious agent that is required to set off infection? If so, does a novel virus, one for which their is presumably no immunity, can we just extrapolate to a zero critical load. For instance, when Ferguson speaks of the low probability of transmission at a public event, is he basing the argument on the low probability of coming in contact with an infected person, or is this an argument based on a dosage and a short interaction is below the critical load?
The study I’m referring to is: https://www.medrxiv.org/content/10.1101/2020.03.05.20030502v1.full.pdf
The viral load refers to the number of copies per volume. “Also, viral load differed considerably. In SARS, it took 7 to 10 days after onset until peak NA concentrations (of up to 5×105 copies per swab) were reached 13,14. In the present study, peak concentrations were reached before day 5, and were more than 1000 times higher”
My understanding is still that all you need is one successful intrusion into a cell to be “infected”. They were only successful growing virus from early samples, never late ones, so the proportion viable was very high early, very low later, even if the quantity of copies was high. Figure “e” was the one I found interesting.
Kevin and Michael
Your comments raise related questions that bear on the transmissibility of this “novel corona virus.” Will a single virus guarantee infection in a susceptible individual, or does infection require some larger number to account for probability of a host cell becoming infected? Are there mechanisms in the body to protect against foreign agents that can defend against a small number potentially dangerous pathogens?
These are important questions because if it takes some finite number of viruses to cause infections, it implies that the length of time around an infected person should be minimized. Also, it implies that any kind of filter, even one that is only 50% effective in removing aerosols, may be better than nothing. These are things that I don’t see being discussed.
I always appreciate your comments, Joe. I had wondered a bit about R0, because of the implied “0” subscript, being an initial value, but introducing different Rs just complicating the picture, and what I wanted was an expression just showing relationships. Besides, Nowak doesn’t distinguish, so I thought I’d follow his lead. Not being connected to the infectious disease research world, I am not aware of that particular model you refer to, but believe it or not, I modified Nowak’s model, and came up with the SIR model on my own — it just made more sense to me and the SEIR model makes even more still.
Your last paragraph is exactly what I was hoping to convey. That modeling with exponential processes is fraught with uncertainty, and a person can find lots of historical examples of it going badly wrong. We might have thought more about the entirety of the issues involved, but maybe there was no time after all the distractions of November through January.
I am surprised at the response to this. We seem to have been completely unprepared; authorities first encouraged terribly wrong behavior and then promptly did a 180; and as one might expect people began using the pandemic to settle political scores even before they could spell “corona”. Stay well and thanks for the new info.
What would justify the current restrictions?
If in 6 weeks there are 50000 deaths in the US (on the order of the Vietnam War) and there are thousands
more dying every day, would you-all think the current restrictions are still an overreaction? What is your
limit?
This is not to mention that many people who eventually recover get very sick and require hospitalization for a long time.
Even if the death rate was 0 it is worth something to avoid sending possibly millions of people to the
hospital at the same time for many weeks and in the process overloading the health system.
I hope the current trajectory moderates, but I’m not looking forward to people claiming that it was all an overreaction if it does.
I don’t see how the curent restrictions can EVER be good policy.
Destroying freedom and the economy is bad policy, period.
Aaron
You are asking a variant of a question I have asked from the beginning: “What is an acceptable loss of lives from seasonal flues?” During any particular year, the US may see something between 20,000 to 80,000 lives lost from seasonal flu, and nobody blinks. The epidemiologists shrug their shoulders and say, “We didn’t do too well on guessing what strains would be a threat this year.” Nobody suggests shutting down the economy when it becomes obvious early in the season that the vaccine was poorly matched to the emergent strains. There hasn’t been any public discussion on what is an acceptable threat, and what should trigger a response as unprecedented as our current lock-downs.
Even when H1N1, and SARS 1, and MERS were circulating, nobody got sufficiently concerned to suspend commerce and freedom of movement. Why? They were “novel” diseases with no history to guide. Our current pandemic of COVID-19 doesn’t come close to matching the loss of 195,000 American lives in October 1918. I’d like to see some public discussion on what risks are acceptable and what are unacceptable, and rationales for the decisions.
I saw a comment from someone 110ish years old, perhaps in the UK prerhap not. To paraphrase “we didn’t have air travel in 1919 but Spanish Flu got right round the world very quickly.” They also had various restrictions in various countries. The UK has a pretty dreadful record on excess winter deaths for as long as records have been maintained, basically since about 1950. This is the last 20 years data
Winter season Excess Five-year
winter moving
deaths average
1998 to 1999 46810 38134
1999 to 2000 48420 34040
2000 to 2001 24790 34236
2001 to 2002 27230 29558
2002 to 2003 23930 26188
2003 to 2004 23420 26268
2004 to 2005 31570 25530
2005 to 2006 25190 25668
2006 to 2007 23540 28250
2007 to 2008 24620 27068
2008 to 2009 36330 27222
2009 to 2010 25660 27322
2010 to 2011 25960 28628
2011 to 2012 24040 24818
2012 to 2013 31150 28430
2013 to 2014 17280 28138
2014 to 2015 43720 30212
2015 to 2016 24500 33864
2016 to 2017 34410 35048
2017 to 2018 49410
My hope is that all the equipment , mainly ventilators, being brought into service will help reduce excess winter deaths in future years in the UK. Hopefully in the aftermath something will be done about bational disgrace of Excess Winter Deaths in the UK.
Ben
You quoted, ““we didn’t have air travel in 1919 but Spanish Flu got right round the world very quickly.” That was probably in part because of the movement of troops from America, England, India, Australia, and other countries to the front lines in France, and then returning them to their home countries at the conclusion of the war in 1918.
Okay, guys, we’re all cooped up. How about a little math problem to break up the monotony?
Specifically, I need help with what the authors of the piece at https://www.statnews.com/2020/04/01/navigating-covid-19-pandemic/ wrote: “If the SARS-CoV-2 virus has a contagiousness of three, meaning every case infects three other people, then we won’t get to the end of the epidemic until two-thirds of the population has become immune by infection or by vaccination.”
Hey, one of those guys is a Harvard epidemiology professor, so I’m sure this is widely accepted in that field. And it sounds plausible; if one person would infect three other people when everyone’s susceptible, then on average he’d infect less than one when susceptibility fall below a third, and the chain would die out.
But to me it seems that initially the dying out would take a while and that instead of two-thirds more like 94% would be exposed because of all those infectious people who still have infecting to do when susceptibility has first fallen below a third.
Obviously, this is their specialty, so presumably they know what they’re talking about. But I don’t get it. Can anyone help me out?
If we take the R0 value as an initial value, then the time dependent R value, whatever those epidemiologists call it, is
if nothing else like U or V or B in my post changes. So,
Correct: More than 2/3 immunity means that we’ve reached the decay stage. But, at least if I’m right, that doesn’t mean that only 2/3 of the population will get the disease.
Perhaps this is just a question of interpretation; I read “end of the epidemic” as meaning that (barring changes in behavior, etc.) only 2/3 of the population will come down with the disease. But maybe that’s not what the authors meant. Maybe they only mean it’s reached the decay stage; maybe they actually agree with me that the decay stage will theoretically persist until 94% of the population has been infected.
Or maybe I’m just wrong.
I think you are correct, I just read it as the authors intended, but as you and I have learned, once we enter this world of bio-medical modeling there is an infinity of ways to not understand what is being asked or answered — and many correct answers.