Exponential Math and the Corona Virus

@georgeob1,

Quote:

I'm not making forecasts of the deaths we may accumulate from this virus because there are simply too many variables that could affect the outcome.

The reason I started this thread is because I believe that you, and several other people are minimizing the seriousness of this crisis.

I am showing that there is a very real possibility that the number of Americans who die of the virus by the end of April could top one million. The fact is that the rate of people in the US dying of the virus has been increasing at fairly consistent exponential rate for weeks. Yes, there are unknowns... but this exponential growth is a fact.

You don't want to make forecasts, fine. Do you accept the real possibility of a million US deaths by the end of April? Does this change any of the political positions you are taking on the other threads?

1 Reply

@maxdancona,

maxdancona wrote:

The reason I started this thread is because I believe that you, and several other people are minimizing the seriousness of this crisis.

1) I am social-distancing and quarantining as much as possible while trying to assess the seriousness, which you seem to already assume you know just based on the media coverage you are uncritically swallowing.

2) The reason you started the thread is because you like math and you want to pretend like it can do more than it can.

Quote:

I am showing that there is a very real possibility that the number of Americans who die of the virus by the end of April could top one million. The fact is that the rate of people in the US dying of the virus has been increasing at fairly consistent exponential rate for weeks. Yes, there are unknowns... but this exponential growth is a fact.

Calling a possibility 'very real' makes it sound more probable, but you haven't analyzed the fit of your mathematical modeling well enough to know how probable your estimates are.

Quote:

You don't want to make forecasts, fine. Do you accept the real possibility of a million US deaths by the end of April? Does this change any of the political positions you are taking on the other threads?

People should take maximum precautions to avoid unnecessary exposure and risk. That said, investing and wasting resources on speculative doomsday scenarios is foolish at best and politically-economically manipulative at worst.

You want to build a fleet of ventilators? Ok, but then do so for free using volunteer labor so that there's no incentive to drum up alarmism to stimulate the ventilator supply-chain.

If people and businesses aren't willing to step up efforts voluntarily and free of charge in this crisis, they are only concerned with their own bottom-line, aren't they?

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@maxdancona,

There are a number of mathematical models for epidemiology. All have a trajectory for active cases that rises to a maximum, generally at the point of inflection of total cases and then tails off - some symmetrically with the rise others indicate a slower and more extended decline after the point of inflection.

Individual cases are far more complex with time-variable changes in infection transmission rates due to things like whether variations and, various temporary restrictions imposed on people s(such as the social distancing measures now in effect

As for the rest you can do your own research.

1 Reply

@georgeob1,

I am only objecting to the use of the word "bell-shaped" curve when referring to a epidemic curve. The term "bell-shaped" curve refers to the Gaussian function. As far as I know the Gaussian function is not the basis for any "mathematical model" for an epidemic curve.

This is a pet peeve of mine. We keep seeing graphics in the media that are clearly based on a Gaussian bell-shaped curve. This is a shape that everyone recognizes. but it is wrong. That mathematics behind that familiar shape are not applicable to the epidemic curve they are representing.

I think it is just a short cut... but it is still wrong. It is confusing two completely different mathematical concepts. Maybe I am being pedantic about this.

1 Reply

@maxdancona,

You are indeed.

These are very complex problems with many independent variables and parameters, like the exponent in the exponential growth rate which so fascinates you, that actually vary significantly in value over time. There are idealized models applicable to simpler cases that ignore these real - life variables. Despite that these idealized cases have some key properties that manifest themselves also in the more complex and messy real life examples that arise. You appear to have little understanding of this complexity and instead focus rather obsessively on single issues.

3 Replies

@georgeob1,

georgeob1 wrote:

You are indeed.

These are very complex problems with many independent variables and parameters, like the exponent in the exponential growth rate which so fascinates you, that actually vary significantly in value over time.

You are getting the math wrong in two ways.

Let's tackle the first. You are saying the "exponent" varies in value over time. That doesn't make any sense.

The exponent is the independent variable (i.e. the number of days). What you you mean to say is that the base, or the growth rate varies significantly over time.

The function is

f(x) = A*B^x

This is often rewritten like this to talk about "growth rate" (since B and R are both constants, this doesn't change the function).

f(X) = A * (1 + R) ^ x

A and B are constants that depend on the specific exponential function.

f(x) = 780 * 1.25992 ^ x

In this we can say the base is 1.25992 and the growth rate is 0.25992. The growth rate is convenient since this is the amount the function changes per unit change in "x". In this case X represents number of days, so to get the value of the next day, you can just calculate X * 0.25992.

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@georgeob1,

What I think you are claiming is that the growth rate is constantly changing. But it isn't. You are simply wrong.

You can look at the data and see what it is actually doing. And, it is not changing significantly. For more than 2 weeks we have seen exponential growth with a fairly consistent growth rate.

You can look at the data for the past two and a half weeks and see this. You are giving speculations about what you think should happen. I am giving you the data showing what has actually been happening.

You can rightly say that we don't know what will happen in the weeks to come, I can't tell the future any better than you can. But I can say that in past two weeks we have seen consistent exponential growth, and that if this continues (and we know idea how long this trend will continue) we will have more than 1 million US deaths by the end of April.

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@georgeob1,

I agree with your point about complexity. And of course you are correct. However, I feel you are minimizing the seriousness of the crisis. It is like seeing the tsunami coming... you know it will be a big disaster even though you can't predict exactly how high up on the land it will reach. If you see the water rising rapidly... saying "well it has to go down sometime" isn't very useful.

Your point that "exponential growth rates... vary significantly over time" is nice but irrelevant. Yes, sometimes exponential growth rates vary significantly and sometimes they are constant. It is very likely that at some point in the future (we don't know when) the growth rate will change.

But in the past weeks the growth rate has been fairly steady. It hasn't been changing significantly. That is a fact that we can measure.

1 Reply

@maxdancona,

I'm not at all sure the changes in the exponential growth rate are insignificant.. For most Western countries the time required to double the case load has dropped from two days in the first three weeks of the epidemic (different start dates in in each country) to three days currently. Evidence is accumulating that the doubling time is still increasing.. All are at much higher infection levels now, and that is a matter of concern. However if the initial exponential growth rate had continued we would have had roughly twice the current infection case load. This is evident if you plot the caseloads in terms of the # of days since the infection started in the country in question.

You are correct that in the early stages of the infection I was putting too much credence on apparent slowdowns in the increase of caseload data. It turned out that some of that was a result of slowdowns in case reporting over weekends, and other parts were merely anomalies in the reporting routines as people in various parts of the country got accustomed to and proficient in the reporting methodologies. A lot of that has washed out now and we have every reason to believe that as widespread testing begins we will see significant increases in our detecting and reporting efficiency. That may appear as an otherwise unexplained increase in the apparent infection efficiency of the virus. Complexity is everywhere.

1 Reply

@georgeob1,

Quote:

For most Western countries the time required to double the case load has dropped from two days in the first three weeks of the epidemic (different start dates in in each country) to three days currently. Evidence is accumulating that the doubling time is still increasing..

This is certainly not true for the US.

It does looks like it is true for many European countries. Of course each country will be different. Italy got hit hard and took some pretty drastic measures (that we are not taking) to slow down the growth rate.

The US has had one of the worst national responses from Western countries. Most countries have had a consistent coordinated national response. We have had mixed messages on the national level and inconsistent response on the regional level. The American media has been doing most of the work of public awareness. In most countries this is done by the national government.

The real message I am I trying to say here is don't minimize this.

1 Reply

@maxdancona,

maxdancona wrote:

Quote:
For most Western countries the time required to double the case load has dropped from two days in the first three weeks of the epidemic (different start dates in in each country) to three days currently. Evidence is accumulating that the doubling time is still increasing..

This is certainly not true for the US.

It does looks like it is true for many European countries. Of course each country will be different. Italy got hit hard and took some pretty drastic measures (that we are not taking) to slow down the growth rate.

The US has had one of the worst national responses from Western countries. Most countries have had a consistent coordinated national response. We have had mixed messages on the national level and inconsistent response on the regional level. The American media has been doing most of the work of public awareness. In most countries this is done by the national government.

The real message I am I trying to say here is don't minimize this.

Are you familiar with Glassner's Culture of Fear book? If not, you should be because you are basically resonating with it.

Both you and the media (and many academics) are biased toward making more significant-sounding information than is necessarily true. I am guilty of this too, but I try to point out often that reasoning involves tentative acceptance of different possible outcomes simultaneously in order to explore different ways of modeling and their possible implications.

What good governments do is try to clarify the level of risk and suggest prudent measures without encouraging panic-reactions.

What commercial media tends to do, on the other hand, is achieve maximum attention-grab value. The reason for this has been explained as relating to the amygdala portion of the brain and the way it tends to focus in on things that trigger fear. The term Glassner uses in Culture of Fear, as I recall is, "if it bleeds it leads."

Alarmism is bad science. Yes, it's important to clarify risks and how things work, but you should also note how, for example, the number of cases are rising at least in part at the rate they are because of more testing and that social distancing and lockdowns necessarily slow down the rate of transmission and thus the spread of the virus.

1 Reply

@livinglava,

Quote:

for example, the number of cases are rising at least in part at the rate they are because of more testing and that social distancing and lockdowns necessarily slow down the rate of transmission and thus the spread of the virus.

You do realize that this makes it worse, right?

1 Reply

@maxdancona,

maxdancona wrote:

Quote:
for example, the number of cases are rising at least in part at the rate they are because of more testing and that social distancing and lockdowns necessarily slow down the rate of transmission and thus the spread of the virus.

You do realize that this makes it worse, right?

Makes what worse? How?

I said two different things:
1) that the rate of infections is growing due to the spread of testing.
That means that the actual rate of infections could be slowed by social-distancing and lock-downs but the numbers would still show an increasing rate as more testing revealed more infections despite the total number of infections growing at a slower rate.

2) that the lockdowns and social-distancing must be working to at least some degree. We cannot measure how well they are working, because we don't have any data that's not affected by changing sampling practices as public information changes, medical awareness grows, and testing changes.

It's like trying to count the rate of growth of a fly population in a room of rotting meat where people are simultaneously cleaning up the meat and thus reducing the number of maggots but also they are turning on more lights so more flies are becoming visible.

The number of flies counted depend on both the changing rate of fly reproduction and maturation as well as the rate at which more light in the room makes more flies visible.

Merely calculating the rate without taking into account the interaction of sampling changes and transmission-cultural changes paints an inaccurate and assumptive picture.

You can work with the data you have, but you shouldn't suggest that it is an accurate representation of reality, only a sketch of an uncritical and biased estimate.

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I think the media is downplaying the crisis (at least the numbers).

Part of this is an effort to avoid panicking the public. The media takes cues from the CDC which is carefully crafting a message during this crisis. If you want to be cynical, the media will get better ratings if the crisis isn't presaged.

I don't see any way that April isn't a horrible month. The numbers of deaths are going to be much bigger than most Americans are expecting... the only question is how big.

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@maxdancona,

May will be pretty bad too I think. And we'll probably have a second wave strike in the fall.

1 Reply

@oralloy,

oralloy wrote:

May will be pretty bad too I think. And we'll probably have a second wave strike in the fall.

From what I am reading, a "second wave" will mean that we fucked up and removed the restrictions too soon. That is what happened in the 1918 Spanish flu.

Hopefully we won't do that.

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@maxdancona,

maxdancona wrote:

I don't see any way that April isn't a horrible month. The numbers of deaths are going to be much bigger than most Americans are expecting... the only question is how big.

I don't recall seeing any graphs of the annual/monthly death rate due to all causes of entire populations.

Before this year, we were having record numbers of opioid deaths, but before that I don't recall any special death-rate boosters.

It is impossible to put these kinds of special death-boosters like COVID19 and/or opioid overdoses in perspective unless you can look at the overall death rate and see how many people were already ripe for death before overdosing and/or contracting COVID19.

The numbers shouldn't falsely suggest that totally healthy people are suddenly dropping dead from COVID19, opioids, etc. without taking into account the longer health struggles that people go through leading up to a final infection and/or opioid overdose.

It is sad that people get sick and die, but we shouldn't treat all deaths like they happened to totally healthy people just because the general death rate is typically ignored by the media as not news-worthy.

Put another way, crises like COVID19 and/or opioid overdoses should be understood in the broader context of the health problems they accompany in individual lives; not as something separate from other health issues.

1 Reply

@livinglava,

Sooo Lava, you would say

Quote:

sorry about your son David but he did have diabetes so his death from a respiratory was kind of expected...

and your grandmother was 75 after all so she was going to die soon anyway

This is a case where you are being both ridiculous and offensive. You have started with your idea that this is "no big deal" which has now become "Truth" to you. So you are making rather twisted arguments to support your "Truth".

However, to most normal people a virus that can kill hundreds of thousands of Americans is a big deal. No one should be minimizing it.

1 Reply

I don't think there is much value in arguments like this. Putting the effects of the Coronavirus in the context of other causes of disease and death is indeed useful. At the same time the reaction of anyone close to the victims of new threats like coronavirus or long standing ones, more familiar to us all, is close and personal.. Both perspectives are valid and meaningful: they aren't in conflict with each other.

1 Reply

@maxdancona,

maxdancona wrote:

Sooo Lava, you would say

Quote:
sorry about your son David but he did have diabetes so his death from a respiratory was kind of expected...

and your grandmother was 75 after all so she was going to die soon anyway

This is a case where you are being both ridiculous and offensive. You have started with your idea that this is "no big deal" which has now become "Truth" to you. So you are making rather twisted arguments to support your "Truth".

What is more ridiculous, offensive, and cruel: telling someone the truth that someone they lost died as a result of complications of a long struggle with known health problems, or telling them that they could have lived longer if it weren't for this new virus that killed them early?

If the truth is that a new virus came along and killed them early, there is no sin and telling the truth. If, however, the new virus is just the focus of attention because it's been identified and studied unlike many other viruses that have similar effects, then that is deceptive and thus offensive and cruel.

Do you remember when kids used to tell each other, "your epidermis is showing," to scare the other kid into thinking it was something bad because they didn't know 'epidermis' just meant the outermost layer of skin?

If this coronavirus turns out to be a garden variety virus like so many others that cause death for some people who are at the tipping point, and the media scares everyone into believing it's an aggressive pandemic, that would be abusive and exploitative, not to mention offensive and cruel.

Quote:

However, to most normal people a virus that can kill hundreds of thousands of Americans is a big deal. No one should be minimizing it.

Putting things in perspective is not 'minimizing' them. Opioids were killing people, but it isn't minimizing anything to note that there are other factors going on that lead to opioid death besides the opioid use/overdose itself. It is the same with any other health threat.

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Exponential Math and the Corona Virus

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