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Mathematics of exponential growth

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(@zebedee)
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I've finally found the time to write up some arguments I've had with people whose grasp of Mathematics is sadly lacking: Why epidemics never grow exponentially

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lordsnooty
(@lordsnooty)
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Posted by: @zebedee

I've finally found the time to write up some arguments I've had with people whose grasp of Mathematics is sadly lacking: Why epidemics never grow exponentially

You may be right to focus on this, but it may not help. In the loose language, used by plain people, an exponential plot is one that gets steeper more and more quickly, and hence is scary, since any plot like that soon resembles skid row, an uncontrollable acceleration to oblivion, which is what the MSM are trying to depict. That is what they mean, not the strictly mathematical version. you are talking about. When one sees a plot like this, it gets steeper and steeper mighty quick as it powered by an exponent.My advice, find something else to worry about.

 

 

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(@zebedee)
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@lordsnooty Exponent is a Mathematical term and I'm a Mathematician so I do find the misuse very irritating.

Having read a textbook on epidemiological modelling my thoughts were that the Maths wasn't very hard and there seemed to be a lot of hand waving arguments.

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lordsnooty
(@lordsnooty)
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Posted by: @zebedee

Having read a textbook on epidemiological modelling my thoughts were that the Maths wasn't very hard 

no it's obvious that if I catch and give it to 10 others, and if they do likewise, it explodes quite quickly until some limits are reached.

 

 

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(@zebedee)
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@lordsnooty

it explodes quite quickly until some limits are reached

I did say the problem was hand waving arguments

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lordsnooty
(@lordsnooty)
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Posts: 636
Posted by: @zebedee

@lordsnooty

it explodes quite quickly until some limits are reached

I did say the problem was hand waving arguments

As we can all l see  you did NOT start  with any  hand wave.If you  pretend to be a mathematician, you should stay with facts and and  not  resort to  to lies. Esp. when lives aare at at  stake, you silly ignorant, stupid, cretin.Sorry to be blunt, but that its what you are. my advice ; pull your  socks up, soonish.

chhers.

 

ste 

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(@zebedee)
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@lordsnooty

Like I said hand waving, also extremely rude and ignorant. Ignorant and hand waving because you ignore the case of significant prior immunity causing an epidemic to start close to its peak. i.e. unremarkable growth followed by decline.

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 jmc
(@jmc)
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@lordsnooty 

 

But the R0 for SARs CoV 2 is not 10, its around 1.2 community spread. 

And the At Risk population for infection spread is not 100% it  is close to 20% due  to very high rates of cross immunity for < 55 population.

So no exponential spread in fact its a very shallow curve with a low maximum and fast decay to a low equilibrium point infection rate. 

This is very basic maths.

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lordsnooty
(@lordsnooty)
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Posted by: @jmc

This is very basic maths.

like i sad it's obvious,

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(@stop-believing-start-thinking)
Joined: 2 years ago

Posts: 202
Posted by: @jmc

@lordsnooty 

 

But the R0 for SARs CoV 2 is not 10, its around 1.2 community spread. 

And the At Risk population for infection spread is not 100% it  is close to 20% due  to very high rates of cross immunity for < 55 population.

So no exponential spread in fact its a very shallow curve with a low maximum and fast decay to a low equilibrium point infection rate. 

This is very basic maths.

Are you quoting R0 = 1.2 for a particular time period, location or variant?

Obviously it is not correct at the moment for the omicron variant.

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 jmc
(@jmc)
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@rational 

All R0's quoted at the moment for omicron are model estimates. The model estimates are based on "case" numbers derived from a screening test that not only has a very high false positive rate but most of the previously used PCR reagent kits dont detect the omicron in true positive samples due to the S protein  mutation.  The only probe match that was high confidence for previous variants.

There is no evidence that the omicron community spread R0 is much different from typical winter flu season respirator infections. Around 1.2. Or that the mix of infection agents is any different from 5 or 10 years ago.

Every winter 1% to 3% of the adult population and over 10% of children have an active respiratory infection at any given time. I've got a probably rhinovirus one at the moment. And at least 10% of all deaths of those over 65 are from these infections.

Every year.

Its just a normal winter flu season.

 

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(@stop-believing-start-thinking)
Joined: 2 years ago

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@jmc 

Ah, you are back to your old theory about false positive rate for PCR tests. What was it last time 99% PFR?

I guess you never got round to looking up the definition of FPR, did you?

Now at the fastest rate of increase (around the time you made up your R=1.2, the doubling time was around 2.5 days.  Doesn't really match, does it.

Then have a look at what's happened in the USA, where there is a good supply of vaccine refuseniks to help things along. Their case rate doesn't look much like flu.

Now if you look closely in the UK, the flu hasn't really happened again.

 

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(@stop-believing-start-thinking)
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@jmc 

It's taken nearly a month to think of an answer and that is the best you can do?

Quote some evidence, rather than just waffle.

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(@stop-believing-start-thinking)
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Posted by: @jmc

@lordsnooty 

 

But the R0 for SARs CoV 2 is not 10, its around 1.2 community spread. 

And the At Risk population for infection spread is not 100% it  is close to 20% due  to very high rates of cross immunity for < 55 population.

So no exponential spread in fact its a very shallow curve with a low maximum and fast decay to a low equilibrium point infection rate. 

This is very basic maths.

But....the highest infection rates are in the younger age groups.

How do you explain that, with your statement above?

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 jmc
(@jmc)
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@zebedee 

The maths is very basic but the modelers  seem to fall into two groups: Those who understand the maths but dont understand the bio-science; and those who understand the bio-science but fail to understand the maths.  The for these two sets is almost a null set. Very very few seem to understand both sides. Which is vital for a useful mathematical model.

The hand-waving of the bio-science people in epidemiology is that they either use maths without understanding the limitations and underlying assumptions of what they are using, or else simplify to the point of irrelevance because the maths required for the model they are creating is beyond their level of expertise.  Very few progress beyond stock use of standard R packages. For accurate models of this type you are very much into PDE territory.

The maths people are worse in that they usually stick in key values in their models without doing even the most basic research of the relevant medical or bio-science literature. Really basic stuff. The criminal incompetence of Ferguson group at Imperial has been discussed here before but for me the defining moment was the model used as the basic for the shutdown in Lombardy and then all of Northern Italy in February 2020. Which started this whole mass hysteria and catastrophe in Europe.

The model assumed an At Risk population of 100% while the Hong Kong data already showed it was only a small subset due to high cross immunity. And the model assumed an asymptomatic rate of 10%. Not the 50% to 70% that was already clear. The clinical pathology of SARs CoV 2 was following the same pattern as the other human corona viruses.  Stick in realistic values and what you have is a very bad short term viral pneumonia epidemic. Which is what happened. 

All the horror stories you heard from Italy at the time, spring 2020, were due politics and  Italy's socialized medical system. So no surge capacity and the initial refusal of other regions to take overflow ICU patients from the North. The medical system collapsed in Lombardy, Piedmont and Emilia-Romagna but was below capacity in most other regions. And that simplistic and wrong model had a lot to do with it. When added to the toxic brew of local politics.

 

 

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(@stop-believing-start-thinking)
Joined: 2 years ago

Posts: 202

 

Consider it from a mathematical point of view. There is no other point of view, worth bothering with.

The plain fact is that the exponent does not stay the same over the course of an epidemic. It changes as the number of susceptible candidates dwindle, the variant changes, the weather changes or the behaviour of people changes.........

The exponential function is simply a basic tool to allow modelling, upon which many other factors are applied to modulate the exponent.

When infections are in decline, then the exponent is less than 1.

 

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lordsnooty
(@lordsnooty)
Joined: 3 years ago

Posts: 636
Posted by: @rational

 

The plain fact is that the exponent does not stay the same over the course of an epidemic.

It's not even the same everywhere at a single point in time.It's basically different everywhere at all times.

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lordsnooty
Posts: 636
(@lordsnooty)
Joined: 3 years ago

@jmc,

The politics  is very basic but the sceptics   seem to fall into two groups: Those who understand the politics  but do not  understand the communications ; and those who understand the communications  but fail to understand the politics.  The  for these two sets is almost a null set. Very very few seem to understand both sides. Which is vital for a useful political  model.

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Posts: 49
Topic starter
(@zebedee)
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It turns out that epidemics grow between zero and exponential according to a logit-normal distribution

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