[math-fun] COVID Calculator
http://gabgoh.github.io/COVID/index.html Complete epidemic calculator, with sliders for various parameters. Model your favorite epidemic! --- If an asteroid were hurtling towards Earth, I guess I'd be playing with the orbital mechanics calculator. At 12:17 PM 3/1/2020, Henry Baker wrote:
Given the spread of the Covid-19, here's how to explain the mathematics of epidemics.
"The 'basic reproduction number' R0 is defined as the expected number of secondary cases produced by a single infection in a completely susceptible population. It is important to note that R0 is a dimensionless number and not a rate."
R0 is the largest eigenvalue of the 'next generation matrix'.
For example, R0=phi=(1+sqrt(5))/2 for Fibonacci's rabbit problem; R0='k' (neutron multiplication factor) in nuclear fission.
Thus, R0 is the *base* of the exponentials & logarithms which occur in the various solutions instead of Euler's 'e'. Clearly, an epidemic won't go 'viral' unless |R0|>1.
"Notes on R0"
James Holland Jones, Stanford University, 5/1/2007
This is nice. The funny thing about all these curve flattening cartoons is that the infection distribution looks like a Gaussian. I then thought that the removed distribution would be an error function, but clearly this is a wrong conclusion due to a combination of my own stupidity and widespread misinformation. The SIR model is nice and easy, and you might want to compare with Einstein rate equations, which are used in laser physics. Just change excited state to sick state. Immunity building is a difference that explains why a laser can operate continuously, while a pandemic eventually dies out. To do so it needs the non-linear S*I term, which says that transmission requires non-zero population of susceptible and infected. The good news is that the SIR ODEs don’t have any singular points. Thanks for sending this, —Brad
On Mar 21, 2020, at 5:48 PM, Henry Baker <hbaker1@pipeline.com> wrote:
http://gabgoh.github.io/COVID/index.html
Complete epidemic calculator, with sliders for various parameters.
Model your favorite epidemic!
--- If an asteroid were hurtling towards Earth, I guess I'd be playing with the orbital mechanics calculator.
At 12:17 PM 3/1/2020, Henry Baker wrote:
Given the spread of the Covid-19, here's how to explain the mathematics of epidemics.
"The 'basic reproduction number' R0 is defined as the expected number of secondary cases produced by a single infection in a completely susceptible population. It is important to note that R0 is a dimensionless number and not a rate."
R0 is the largest eigenvalue of the 'next generation matrix'.
For example, R0=phi=(1+sqrt(5))/2 for Fibonacci's rabbit problem; R0='k' (neutron multiplication factor) in nuclear fission.
Thus, R0 is the *base* of the exponentials & logarithms which occur in the various solutions instead of Euler's 'e'. Clearly, an epidemic won't go 'viral' unless |R0|>1.
"Notes on R0"
James Holland Jones, Stanford University, 5/1/2007
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Re: "a pandemic eventually dies out" There's been a worrisome number of COVID19 cases where people are *re-infected* weeks after testing negative. So an appropriate mathematical model may have to allow for a more-or-less constant background of residual infections. At 04:51 PM 3/21/2020, Brad Klee wrote:
This is nice.
The funny thing about all these curve flattening cartoons is that the infection distribution looks like a Gaussian.
I then thought that the removed distribution would be an error function, but clearly this is a wrong conclusion due to a combination of my own stupidity and widespread misinformation.
The SIR model is nice and easy, and you might want to compare with Einstein rate equations, which are used in laser physics. Just change excited state to sick state.
Immunity building is a difference that explains why a laser can operate continuously, while a pandemic eventually dies out.
To do so it needs the non-linear S*I term, which says that transmission requires non-zero population of susceptible and infected.
The good news is that the SIR ODEs don't have any singular points.
Thanks for sending this,
ÂBrad
On Mar 221, 2020, at 5:48 PM, Henry Baker <hbaker1@pipeline.com> wrote:
http://gabgoh.github.io/COVID/index.html Complete epidemic calculator, with sliders for various parameters. Model your favorite epidemic! --- If an asteroid were hurtling towards Earth, I guess I'd be playing with the orbital mechanics calculator. At 12:17 PM 3/1/2020, Henry Baker wrote: Given the spread of the Covid-19, here's how to explain the mathematics of epidemics.
"The 'basic reproduction number' R0 is defined as the expected number of secondary cases produced by a single infection in a completely susceptible population. It is important to note that R0 is a dimensionless number and not a rate."
R0 is the largest eigenvalue of the 'next generation matrix'.
For example, R0=phi=(1+sqrt(5))/2 for Fibonacci's rabbit problem; R0='k' (neutron multiplication factor) in nuclear fission.
Thus, R0 is the *base* of the exponentials & logarithms which occur in the various solutions instead of Euler's 'e'. Clearly, an epidemic won't go 'viral' unless |R0|>1.
"Notes on R0"
James Holland Jones, Stanford University, 5/1/2007
https://www.snopes.com/fact-check/covid-19-reinfection/ https://www.npr.org/sections/goatsandsoda/2020/03/20/819038431/do-you-get-im... Allowing for mutation, it is possible to have steady-state solutions, as happens w/ seasonal flu. However, this introduces a new time constant, which we would usually guess to be relatively large. A truly frightening scenario is one with an extremely adaptive super-virus whose successful mutation time roughly matches time of human immunization response. Let’s hope this possibility remains science _fiction_! —Brad
On Mar 21, 2020, at 8:36 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
There's been a worrisome number of COVID19 cases where people are *re-infected* weeks after testing negative.
Do you have a reputable source for this?
-tom _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I think it's been attributed to false positive initial tests followed by a true negative and a true positive. Brent On 3/21/2020 6:36 PM, Tomas Rokicki wrote:
There's been a worrisome number of COVID19 cases where people are *re-infected* weeks after testing negative.
Do you have a reputable source for this?
-tom _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
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Brad Klee -
Brent Meeker -
Henry Baker -
Tomas Rokicki