Coronavirus

[Andrew Slater]

In a true exponential, the rate of change, the rate of change of the rate of change, and the rate of change of the rate of change of the rate of change (and so on) are all constant.

Are you sure that's what you mean about constants? If the rate of change is constant then the rate of change of the rate of change is zero (which admittedly is constant).

I think that the definition of exponential growth is that the instantaneous rate of change is proportional to the instantaneous value, which means that the rate of change is a constant multiplied by the instantaneous value, i.e. for a value increasing with time the rate of change also increases with time (and therefore so does the rate of change of rate of change etc.)

[Frances_iom]

I think Dave2002 has forgotten his elementary analysis d^n/dx^n (a^) = a^n . e^ax
where ^ = raise to power
thus d^2/dx^2 (ie 2nd derivative) of e^ax = a^2.e^ax ie also an exponential function

more details of this + thousands of other functions in Abramowitz + Stegun "Handbook of Mathematical functions"

[Simon B]

IIRC, some mathematicians (possibly all good ones) will tell you that the very definition of e^x is that it is its own gradient function - where e = Euler's number ~= 2.71828. The general case where the base of the exponent is some other constant is, just, well, extra fiddling about. The principle is the same. Draw a graph of any exponential to see that the gradient monotonically increases forever and therefore so does the gradient of the gradient function and so on for an infinite number of derivatives.

This is why it's true to say that unless the infection rate of an epidemic keeps on increasing forever, it is no longer accelerating and is falling away from exponential growth - i.e. R is falling over time.

Anyway, maybe this is just the thread being hijacked by a few of us arguing about maths to distract ourselves from the abundant mayhem in reality .

More interestingly (perhaps) it appears that Prof Spector and his team have rejigged their model to re-establish correlation with the "official" data having noticed that for the first time they've become decoupled, only for the official data to then immediately seem to start doing what he said it was going to in the first place. For now. Maybe.

In summary, nobody knows. Once again, wait and see in the hope that Johnson & Co haven't bodged it again with a further volte-face to come soon but not soon enough...

[vinteuil]

In summary, nobody knows. Once again, wait and see ...

... I like the fact that various of the French epidemiologists and other scientists are now saying that we may see something approaching normality in the spring of - 2023


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[teamsaint]

... I like the fact that various of the French epidemiologists and other scientists are now saying that we may see something approaching normality in the spring of - 2023


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Goalposts moving further than ever.

But the moving of the goalposts almost seems to be the point now.

Age standardised mortality for the first half of 2021 was very broadly in line with most other recent years. See fig 5 .

https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/bulletins/monthlymortalityanalysisenglandandwales/june2021

IMO, covid now needs to take its proper place in the range of healthcare issues that we need to address, including other respiratory disease.

[french frank]

IMO, covid now needs to take its proper place in the range of healthcare issues that we need to address, including other respiratory disease.

'Its proper place', being the point at issue. On the basis of the evidence, what is 'its proper place'?

[teamsaint]

'Its proper place', being the point at issue. On the basis of the evidence, what is 'its proper place'?

That’s a judgement call of course. But given the level of deaths in the last few months compared to other respiratory disease ( for example) and the age standardised mortality figures, its proper place might be thought to be much lower in terms of govt intervention than currently, esp give that the vaccine booster drive will kick in before long. We are givingbpeople the support and interventions they need to feel as safe as is reasonable, just IMVHO.
There are a lot of important calls on health resources, and sooner or later we must learn to live with endemic covid. And that doesn’t mean a vast infrastructure of intrusive govt IT, IMO, which will do far more harm than good , long term.

[french frank]

That’s a judgement call of course. But given the level of deaths in the last few months compared to other respiratory disease ( for example) and the age standardised mortality figures

I share your general distrust of government policies, but I'm not sure I agree with your analysis of the current situation.

[teamsaint]

I share your general distrust of government policies, but I'm not sure I agree with your analysis of the current situation.

I’m not really sure what my analysis of the current situation is, certainly not in detail. But we definitely ( all of us) need to learn as we go through this, and try to draw what sensible lessons we can from history.
However, when age standardised mortality is broadly level with many previous years, including a big peak of covid deaths in early 2021, the conclusion that we need to start rebalancing our healthcare efforts and social regulation, with one eye on the political and societal collateral damage , seems to me inescapable.

[Dave2002]

IIRC, some mathematicians (possibly all good ones) will tell you that the very definition of e^x is ....

Oops!

I think I could just say that the exponential function in the space of all real valued functions is a fixed point under the operation of differentiation.

[Serial_Apologist]

Oops!

I think I could just say that the exponential function in the space of all real valued functions is a fixed point under the operation of differentiation.

Couldn't have put it better meself, errm........

[teamsaint]

Talking of integration, or lack of it, the government has the assistance of the PL in leading the charge towards vaccine passports. The Telegraph is reporting that double vaccination will be required to attend a PL match from October. No testing option , just the vaccinations, plus the autumn booster presumably.

Really sinister . It won’t end at sports stadia. We really should be very, very concerned.

It is possible that this is all bluster to get more youngsters to sign up for vaccination But the idea that the govt could even bluster in this way is truly reprehensible.

[LMcD]

Talking of integration, or lack of it, the government has the assistance of the PL in leading the charge towards vaccine passports. The Telegraph is reporting that double vaccination will be required to attend a PL match from October. No testing option , just the vaccinations, plus the autumn booster presumably.

Really sinister . It won’t end at sports stadia. We really should be very, very concerned.

It is possible that this is all bluster to get more youngsters to sign up for vaccination But the idea that the govt could even bluster in this way is truly reprehensible.

It's certainly reprehensible, but it surely comes as no surprise.

[Bryn]

Talking of integration, or lack of it, the government has the assistance of the PL in leading the charge towards vaccine passports. The Telegraph is reporting that double vaccination will be required to attend a PL match from October. No testing option , just the vaccinations, plus the autumn booster presumably.

Really sinister . It won’t end at sports stadia. We really should be very, very concerned.

It is possible that this is all bluster to get more youngsters to sign up for vaccination But the idea that the govt could even bluster in this way is truly reprehensible.

Seems an entirely proper public health measure, to me. What is so leftist about it? Attendance at PL games is not an essential contribution to society and they have considerable potetial to stread air-born diseases such a COVID-19.

[french frank]

Seems an entirely proper public health measure, to me. What is so leftist about it? Attendance at PL games is not an essential contribution to society and they have considerable potetial to stread air-born diseases such a COVID-19.

I don't write off team's warnings, but as far as the UK government is concerned, vide: https://www.theguardian.com/world/20...-delta-variant

'... authorities from Greece to Italy and France to Portugal are bringing in what are effectively vaccine passports for a wide range of activities, although most are shying away from using that term, which has become incendiary.'