so it is certain to grow exponentially for rthe first steps, petering out with high number of steps as the choice of susceptibles shrinks. how mant steps have there been so far?
Better to say that there is only ever sub-exponential growth.
In any case sub-exponential growth is eaily enough to swamp any practical sort of affordble health system.
If an epidemic is growing, it is exponential growth ( where the exponent is >1 ) . The exponent will reduce as the population acquires immunity, until it is less than 1. Once this is reached the epidemic is in exponential reduction (where the exponent is <1)
As explained on YouTube https://www.youtube.com/watch?v=p1lyggPhWOM
As well as using an unrealistic small population, he is calculating the odds of a person infecting 2 people. That is not the test!
A person only needs to infect more than 1 person for exponential growth. i.e. 1.00000001 is enough thechnically.
No.
Bolton has shown there will be a rise in cases but few hospitalisations and deaths. Bolton is now clearly on the downward trend. I don't have the data for when the Bolton 'spike' started - but it seems quite short - my guess is the whole thing once finished will have been 6 weeks.
The local areas seeing rises and more focused in South Asian communities (which is not representative of the country at large).
It takes 3 weeks from contact> infection > symptoms> test > result on website. These results are from the bad weather period 3 weeks back. After 3 weeks the current sunny, dry weather should dent the rises.
My guess is Boris will be forced to delay but on 21 June, cases will be going down.
Choosing a small population for his basic sums, allows the herd immunity to reached very quickly. He should do it for a population equating to a large city, then consider the time frame for each infection/recovery cycle. Then you will get an estimate of reality.
His trivial sample size is selected to deceive.
Choosing a small population allows for some accuracy when doing the illustrative products and divisions. By the second step certainty of exponential growth has gone as noted in the formulae. If exponential growth does occur then herd immunity is never achieved as everyone becomes infected but I'll agree that it is over very quickly.
If you care to do a proper stochastic simulation then you'll see sub-exponential growth just like you see for example in Anonymous, 1978, Influenza in a boarding school, British Medical Journal, 1:578.
Have you got anything worthwhile to say?
Choosing a small population for his basic sums, allows the herd immunity to reached very quickly. He should do it for a population equating to a large city, then consider the time frame for each infection/recovery cycle. Then you will get an estimate of reality.
His trivial sample size is selected to deceive.
Choosing a small population allows for some accuracy when doing the illustrative products and divisions. By the second step certainty of exponential growth has gone as noted in the formulae. If exponential growth does occur then herd immunity is never achieved as everyone becomes infected but I'll agree that it is over very quickly.
If you care to do a proper stochastic simulation then you'll see sub-exponential growth just like you see for example in Anonymous, 1978, Influenza in a boarding school, British Medical Journal, 1:578.
Have you got anything worthwhile to say?
Choosing a small population is a method to amplify the effect and illustrate the principle to people who don't understand the maths.
Your example of a boarding school is another example with a small population and is just another example of the same situation.
Try doing it with a population of 1 million and see how many steps it takes! That is what is actually applicable to the pandemic.
