E
EddieM
Well as I said I don't know, but some here have disagreed.
Does anybody think a 2nd spike is likely
- Thread starter Notch7
- Start date
Well as I said I don't know, but some here have disagreed.
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D
durhamplumber
an individual, after getting infected, infects exactly {\displaystyle R_{0}}
new individuals only after exactly a time {\displaystyle \tau }
(the serial interval) has passed, then the number of infectious individuals over time grows as
{\displaystyle n_{E}(t)=n_{E}(0)\,R_{0}^{t/\tau }}
or
{\displaystyle \ln(n_{E}(t))=\ln(n_{E}(0))+\ln(R_{0})t/\tau .}
The underlying matching differential equation is
{\displaystyle {\frac {dn_{E}(t)}{dt}}=n_{E}(t){\frac {\ln(R_{0})}{\tau }}.}
or
{\displaystyle {\frac {d\ln(n_{E}(t))}{dt}}={\frac {\ln(R_{0})}{\tau }}.}
In this case,
{\displaystyle R_{0}=e^{K\tau }}
or {\displaystyle K={\frac {\ln R_{0}}{\tau }}}
.
For example, with {\displaystyle \tau =5~\mathrm {d} }
and {\displaystyle K=0.183~\mathrm {d} ^{-1}}
, we would find {\displaystyle R_{0}=2.5}
.
If {\displaystyle R_{0}}
is time dependent
{\displaystyle \ln(n_{E}(t))=\ln(n_{E}(0))+{\frac {1}{\tau }}\int \limits _{0}^{t}\ln(R_{0}(t))dt}
showing that it may be important to keep {\displaystyle \ln(R_{0})}
below 0, time-averaged, to avoid exponential growth.
If you wish to be precise Eddie...spot of Calculas for you.
{\displaystyle n_{E}(t)=n_{E}(0)\,R_{0}^{t/\tau }}
or
{\displaystyle \ln(n_{E}(t))=\ln(n_{E}(0))+\ln(R_{0})t/\tau .}
The underlying matching differential equation is
{\displaystyle {\frac {dn_{E}(t)}{dt}}=n_{E}(t){\frac {\ln(R_{0})}{\tau }}.}
or
{\displaystyle {\frac {d\ln(n_{E}(t))}{dt}}={\frac {\ln(R_{0})}{\tau }}.}
In this case,
{\displaystyle R_{0}=e^{K\tau }}
For example, with {\displaystyle \tau =5~\mathrm {d} }
If {\displaystyle R_{0}}
{\displaystyle \ln(n_{E}(t))=\ln(n_{E}(0))+{\frac {1}{\tau }}\int \limits _{0}^{t}\ln(R_{0}(t))dt}
showing that it may be important to keep {\displaystyle \ln(R_{0})}
If you wish to be precise Eddie...spot of Calculas for you.
E
EddieM
an individual, after getting infected, infects exactly {\displaystyle R_{0}}new individuals only after exactly a time {\displaystyle \tau }(the serial interval) has passed, then the number of infectious individuals over time grows as
{\displaystyle n_{E}(t)=n_{E}(0)\,R_{0}^{t/\tau }}
or
{\displaystyle \ln(n_{E}(t))=\ln(n_{E}(0))+\ln(R_{0})t/\tau .}
The underlying matching differential equation is
{\displaystyle {\frac {dn_{E}(t)}{dt}}=n_{E}(t){\frac {\ln(R_{0})}{\tau }}.}
or
{\displaystyle {\frac {d\ln(n_{E}(t))}{dt}}={\frac {\ln(R_{0})}{\tau }}.}
In this case,
{\displaystyle R_{0}=e^{K\tau }}or {\displaystyle K={\frac {\ln R_{0}}{\tau }}}.
For example, with {\displaystyle \tau =5~\mathrm {d} }and {\displaystyle K=0.183~\mathrm {d} ^{-1}}, we would find {\displaystyle R_{0}=2.5}.
If {\displaystyle R_{0}}is time dependent
{\displaystyle \ln(n_{E}(t))=\ln(n_{E}(0))+{\frac {1}{\tau }}\int \limits _{0}^{t}\ln(R_{0}(t))dt}
showing that it may be important to keep {\displaystyle \ln(R_{0})}below 0, time-averaged, to avoid exponential growth.
If you wish to be precise Eddie...spot of Calculas for you.
Well, it's nearly legible, but doesn't display properly, and it mentions time interval, but not what that time interval is.
No it isn't. The time base for R is determined by the infection in question.
Really it should be bloody obvious it's not a daily R, as then one month and a day after the second person had it (with the relatively low R of 1.6), everyone in the UK would.
R is the number of people you infect whilst you have the disease. Not how many you infect each day.
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EddieM
So that makes R values for different diseases incomparable?
Just skimmed an article about it, seems the R number is a very debatable indicator of anything. Lies, damn lies and statistics I guess.
No, it means that comparing the rate at which a disease spreads is more complex than just taking the R value and counting days.
To take an example HIV/AIDS has an R0 of 2-5. Which is why as team America says, everyone had aids by July 1981.
D
durhamplumber
Bolox..
R is also an indication of how is infectious the disease is..R is NOT Ever the number of people in total one would infect...That is rubbish
D
durhamplumber
Hogshít...If you have the disease and you go within 2metres of 2 people every day for 15mins or so....chances are every day you could infect another 2..and so on.....day 1...1 person infected 2 others....day 2 , 3 people total infect another 2 each......so on......that is why v small changes in R make huge difference....But some infections are worse than others..ie more infectious...Measles...R is 18..ie v v infectious...Differing R meanings too.
D
durhamplumber
Aids is not transmitted very easily at all compared to Covid 19..Blood tranfusion or sex to contract aids.
E
EddieM
Well I'm confused now. I have maths abilities up to 2nd year university (long time ago)
D
durhamplumber
What happened in the third year? You get kicked out?
E
EddieM
No, subsidiary subject, main degree was Chemistry, theoretical mainly, it's quite mathematical, but for a first degree it doesn't require you to do a full degree in maths. If you took it forward however.....
Ive certainly heard a scientist saying that is a likely explanation.
All ages spread it so the more there are the more older people who will get infected. There is some spread in total infections with age but people just concentrate on death figures. Fine but time spent in hospital has a distinct bearing on how well people are when the are discharged. The catch is ventilation. One ICU doctor summarised it by saying take a 20year old marathon runner - it will take 6months for them to recover. The chances of this happening seems to start in the 40's and get more likely with age. Sort of thing a physio may expect people to do at home - stand at the bottom of the stairs, 1 foot on 1st step, 2nd on step, reverse stepping down.
Also of course if it was just left to run the NHS would be over run. That means many that should have gone into hospital would die over a wide age group. The 65+ population might even do that all on it's own.
Death figures at 80+, 41,412 infected 19,043 died.
40-49 17,881 infected 535 died but that not the entire story really. Need a better graph but ~650 40-49's out of a total of 4,127 all ages needed hdu/icu
I think we are due for spikes and far worse than that if people don't take distancing seriously. Tomorrow might show a bit of a surge in London going on last weeks results. It seems that of late some don't care and are blaming Cummins. Signs of stupidity in my view but results from polls do depend on the question asked.
For testing Boris read out the old I have it and ring 111 symptoms less short of breath. I wondered about persistent cough. Cough sure but persistent? They are concerned that not many are coming forwards to be tested.
Out of interest it seems some people from care homes etc did die in hospital. Haven't found any info on numbers.
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