Why aren't we all infected yet?

Exponential growth is exponential growth, no matter what the rate is. Maybe epidemiologists should refer to the term "doubling time", because that would make it more clear to the population what the danger is.

I've been warning on the dangers of exponential covid19 growth on here for weeks, even when people still said the numbers are low, exponential growth is not proven, everything is under control etc. I even showed the math, and, unfortunately, my initial math predictions were way too low, because of the lack of testing didn't allow estimation of the rate constant.

The trouble is, people just don't understand the principle of exponential growth. At the start, the numbers look very low and they deceive people that everything is fine, basically complacency. That's exactly what happened in this outbreak, so there was no urgency to change behavior. Now, that the numbers get scary very quickly, people are finally changing their tune. Unfortunately, considering the math of exponential growth, it is now almost too late already.

 

It is a mathematical concept and has an exceedingly precise meaning. You are correct that there is a time element involved and the reports ought to indicate some such parameter as doubling time.

One poster here calculated the doubling time as 7 days. Gov. Newsome of CA implied a doubling time of about 4 days.

Now, I know nothing about epidemiology but it seems to me the doubling time depends a lot on local conditions.

 

The relevant math is Farr's Law, which I just looked up.

Here is a blogger who describes Farr's Law

https://douglaswinslowcooper.blogspot.com/2020/03/corona-virus-and-farrs-law.html

 

My wife won't let me pick out the vegetables. She's the expert and I have no idea what I'm doing, she says. Lot of truth in that, too.

 

X is 1,2,3,4,5,.....
It increases by one in the time it takes all newly infected people to infect RO people.
The time will approximate the time it takes for an individual to develope a large viral load and start shedding a high load of virus. In this case we know this is a couple of days.

So say every 3-4 days each person can infect 3 people average(RO=3). The function is 3^x with x increasing by one every 3-4 days.

The first case in the US was diagnosed Jan 19. Likely that patient had already infected 3 people so x=1 at that point. Also it is likely that he wasn't the only individual spreading disease at that time, so there is an additional multiplication factor.

But assuming he was the only one,
It's been 60+ days. X is potentially 15-16 by now
That's 3^16
Potentially 43,046,721 innoculated with virus by now.
In 9-12 more days that's more than one trillion.


So obviously that is impossible, but you can see that that globally, likely many tens of millions are infected. Maybe hundreds, a small fraction of the earth's population btw.

If mortality were 1% as advertised, we'd be looking at a millions dead. So the 1% mortality figure is ludicrous.

 

That maybe true. It's also pointless

Even someone immune to the virus WILL still carry it.

 

Deaths are not growing at the same rate.
The claimed mortality of 1% is highly exagerated.

And the claimed 0.1% mortality for influenza is based on estimated cases, while idiots are claiming 1% Covid-19 mortality based on confirmed cases only.

As a researcher you should see the problem with that

 

My guess is the fact that many people are working from home thereby less people being exposed.

 

It depends on testing facilities and how fast results can be announced. For instance, yesterday the CoronaVirus count in New York City was around eight thousand while today it is twelve thousand. Did that many more people get infected overnight? No. It just means that the results finally came in for the additional people tested.

 

There is certainly a lot of noise in the numbers.

 

It's all in the variables, I agree. What percentage of a region has been tested? What percentage of those tested and found infected inside a region are in the age or health impaired range considered most likely to die from the infection versus numbers of younger and innately healthier people in the same region? So forth and so on.

In addition, where is the testing being done from region to region? Are some areas swamped with testing whereas others are able to handle the influx? Are all testing facilities equal in skill level and equipment?

 

And be spreading it?

 

Yes, there are a large number of infected people we don't know of. However, death is a lagging indicator, it will take two more weeks to get a more precise measure of the number of deaths. Therefore, it is premature to claim that the death rate will be below 1% in the US. Looking at other countries, I wouldn't be as optimistic.

 

I agree, however, it seems to me that in truth, there are an awful lot of Covid 19 cases that exist worldwide that have not been officially diagnosed, while similarly, the number of deaths is likely mostly correct. Obviously we have no way of quantifying precisely, but that rate of non diagnosed cases could easily be half or even MUCH more. When you change the numerator (the number of Covid cases) in the death rate calculation by an inarguably large amount, the resulting death rate is going to change DRASTICALLY.

Surely, the actual death rate is far lower than the confirmed case/deaths from any country would indicate. When we provide the death rate for the flu, we use an estimate of flu cases, and not actual diagnosed flu cases, because only a tiny fraction of flu cases actually get officially diagnosed. It is fundementally flawed how we are currently comparing the death rate from flu where the number of flu cases are estimated,versus the death rate from Covid 19, where the number of Covid 19 cases are only actual diagnosed cases.

 

The time lag from inoculation until death doesn't change. This time can be up to 17 days.
This thing has been spreading since fall.
First Covid(+) documented deaths were in the fall.
If death rate were 1%, the growth in deaths would approximate 0.01(RO^x) from the point that deaths were first documented, which is 17 days or less from the point of first inoculation.

If RO were 2-3, there are literally hundreds of millions now spreading the virus, as viral load is high with individuals shedding large quantities of virus within a few days of inoculation.

And death rate is being calculated based on documented cases and we all know that the 0.1% death rate for influenza is based on estimated cases not documented cases.
So comparing relative rates of 1% to 0.1%, when the numbers aren't even based on the same measurement, is nonsensical.

 

Exactly correct.
Comparing 1% to 0.1% is meaningless when the inclusion groups in the studies are not measuring the same thing.

 

"Exponential growth is exponential growth, no matter what the rate is."

OK that statement seems meaningless because it doesn't tell me what the rate of growth is, and don't say "it's exponential." That's like saying, "it has electrolytes."

As of today's numbers, there are 27,630 cases in the US. The cases were approximately half that on March 19th, so that seems a doubling of the growth rate every three days. Will it continue to be three days? Will it change to doubling every two days? If you don't have the rate of growth, you are not providing any real actual information. And I had to figure out myself that the growth rate was three days. It seems that's fairly valuable data that should be included in briefings.

 

Well I figured 3 days nationally, but that's only because I've been keeping copies of the daily numbers for the US. That doesn't seem to be a considered important information for some reason.

 

The original death rate of 2% was based on no one being immune, so it does matter on what the eventual death rate turns out to be.

 

Of course, the rate is important. However, that doesn't change the equation for the calculation. N = N0*exp(kt).

Here is my math from another thread, from about 3 1/2 weeks ago:

1 50
2 150
3 450 1,500, last Thursday
4 1350 7,800, today
5 4050
6 12150
7 36450
8 109350
9 328050
10 984150
11 2952450
12 8857350
13 26572050
14 79716150
15 239148450

That math assumed a tripling of cases every week. We are in week 4. You see that even with that conservative estimate, it would only take 11 more weeks from now until almost everyone is infected. Of course, that doesn't take into account the likely slowing of the rate when social distancing effects really kick in.

Here is a graph of how the rate affects the growth:

 

Why is it so important what the exact death rate will be? I already conceded that it will not be known until this whole outbreak is over.

Here is the lowdown:

There is a lot more downside of underestimating the death rate, than there is upside of overestimating it. Without knowing the exact value, we should err on the side of caution, rather than telling people that everything is okay, they only have a 0.1%

 

OK for whatever reason, we don't seem to agree on the importance of the rate of growth. I dunno, but that seems vitally important to me, however if they are ignoring it in official briefings and I'm the only one who's complaining...

 

It's also possible there's a lot more Trekkies out there than previously estimated that still haven't left their parents basement and won't for decades. That definitely skews the infection rate way down.

 

Because we dont know the exact variablesor have accurate numbers of cases does not mean it's not exponential growth

The growth equation =(RO)^x

RO is claimed to be about 3
X increases by one every couple of days as newly infected individuals start shedding large quantities of virus.

You should be able to see from this that reported cases grossly underestimate actual cases, and the death rate is much lower than reported

 

I agree with that doctor's theory. It was noted that only 20% of people on the Diamond Princess got infected.

People's immune system are fairly unique to the individual. My neighborhood has a lot of poison ivy, poison oak and Virginia Creeper. I can go out without gloves or any other precautions to knock it down in the spring and fall, and none of those plants have caused a reaction. I had a neighbor a few years ago who almost went into anaphylactic shock just from brushing his ankle against one of those plants, and had a nasty severe rash for weeks. I have read that you can go for years or decades with no reaction to poison ivy, then one year it can suddenly "get you".

Anyway, everyone does need to act as if no one is immune right now, because who knows if, who, or why someone might be immune versus an asymptomatic carrier/spreader.