Coronavirus in the UK - news, lockdown and discussion

[PD58]

Perhaps you should remind yourself what exponential means

Isn't it that the rate of change per unit of time is proportional to the current value of whatever is being measured - which to me will means that today the number of deaths in Italy will be over 700 and tomorrow over 1400 if growth is exponential as the unit of time on the graph being used is one day....?

 

[two sheds]

as the unit of time on the graph being used is one day....?

why this?

 

[Steel Icarus]

Isn't it that the rate of change per unit of time is proportional to the current value of whatever is being measured - which to me will means that today the number of deaths in Italy will be over 700 and tomorrow over 1400 if growth is exponential as the unit of time on the graph being used is one day....?

No. Exponential just means a multiplier, not addition. So a 30% rise on an amount each day on a figure, i.e. cases of coronavirus, would mean larger jumps each day as it's 30% of a bigger number every time.

 

[two sheds]

Indeed: doubling every two days would be exponential growth, as would doubling every week.

 

[SpookyFrank]

Isn't it that the rate of change per unit of time is proportional to the current value of whatever is being measured - which to me will means that today the number of deaths in Italy will be over 700 and tomorrow over 1400 if growth is exponential as the unit of time on the graph being used is one day....?

Effectively it means n(tomorrow) = n(today)x where x is basically any number. Estimates for where the UK is at the moment seem to put x at about 1.4, so not doubling daily but increasing by a greater absolute number of cases every day. The alternative would be arithmetic growth, in which a constant number of cases were added per day, something that doesn't really happen in nature, or only appears to happen at a specific point on an exponential growth curve as x declines over time.

 

[two sheds]

Effectively it means n(tomorrow) = n(today)x where x is basically any number. Estimates for where the UK is at the moment seem to put x at about 1.4, so not doubling daily but increasing by a greater absolute number of cases every day. The alternative would be geometric growth, in which a constant number of cases were added per day, something that doesn't really happen in nature, or only appears to happen at a specific point on an exponential growth curve as x declines over time.

geometric = arithmetic?

 

[Numbers]

Some of the Urban Fam are wary of you PD58

 

[SpookyFrank]

geometric = arithmetic?

Yes I meant to say arithmetic. A level maths was a while ago now. Geometric is actually synonymous with exponential in this context.

 

[two sheds]

change it in the original, nobody will notice

 

[SpookyFrank]

I'm sure this pinch of salt has been added many times but still, worth saying again that there are any number of reasons why the observed case rate and the actual case rate may differ greatly from each other. Incubation period, possibility of asymptomatic cases, effectiveness and availability of testing etc.

 

[kebabking]

I seem to recall that WHO/PHE/CDC version of 'wildfire epidemic' was a doubling of cases every 6 days - and that goes for something like Ebola - no one, to my knowledge, talks about a doubling each day being some kind of definition of exponential growth/decent epidemic status....

 

[sptme]

See that curve, that's what exponential growth looks like in a graph. (South Korea looks like their growth is no longer exponential, so good for them)

 

[weltweit]

There was an interesting point raised in the interview I watched tonight which was that when testing is able to ascertain people who have had the virus and are now immune, it could be these people that are asked to help care for people in vulnerable groups, whether that be doing shopping for them or the like.. because at that stage they would be much less likely to infect anyone else.

 

[PD58]

Not to turn the thread into a maths discussion but here are the figures for Italy on a daily basis (this is the time being used on which the exponential growth calculation would be based) since the first death. It might be me but I do not see except for the first 4 days any pattern of exponential growth ie the growth is not increasing at a constant rate whatever that might be (I am aware it does not have to be double but initially here it was) - for the first 4 days it was doubling so exponential - but then the total went up by 4/8 followed by 5/12, 5/17, 2/11 etc.....so considering this data on a daily basis I cannot see how the growth is exponential but then as someone said maths was a long time ago and i have forgotten most of it. Given this is a medical outbreak though it would be very odd if it was exponential growth.

Date

21​

22​

23​

24​

25​

26​

27​

28​

29​

1​

2​

3​

4​

5​

6​

7​

8​

9​

Nos of deaths

1​

1​

2​

4​

4​

5​

5​

4​

8​

11​

11​

27​

22​

47​

49​

36​

133​

97​

Total

1​

2​

4​

8​

12​

17​

22​

26​

34​

45​

56​

83​

105​

152​

201​

237​

370​

467​

 

[two sheds]

Graph of the daily increase from your figures (assuming my additions are right). Averaging out looks exponential to me, particularly given the last few days.



You keep stressing exponential needs to be doubling every day - it really doesn't.

 

[elbows]

Given this is a medical outbreak though it would be very odd if it was exponential growth.

Maths is often useful because it does a good job of approximating things that can be seen in nature too.

Just google something like 'viruses exponential growth' and you should have no shortage of reading material.

 

[two sheds]

Yep it was a revelation to me when I realized (late on) that exponential means 'grows at a rate proportional to itself'

 

[sptme]

Date

21​

22​

23​

24​

25​

26​

27​

28​

29​

1​

2​

3​

4​

5​

6​

7​

8​

9​

Nos of deaths

1​

1​

2​

4​

4​

5​

5​

4​

8​

11​

11​

27​

22​

47​

49​

36​

133​

97​

Total

1​

2​

4​

8​

12​

17​

22​

26​

34​

45​

56​

83​

105​

152​

201​

237​

370​

467​

Pick any number after the 25th of February and double it. (Eg 12 fatalities on the 25th X2 = 24) Then look at the number of fatalities 3 days later. It's larger than double (26 fatalities on the 28th of February) this means it's doubling rate is faster that 3 days. Doubling every 2 and a bit days is scary fast.
Edit for typos

 

[ska invita]

Does anyone have a good summary of what lockdown looks like in Italy?
What are the rules?

 

[Saffy]

Not officially but this was from my friend whose sister is in north Italy.

From my sis: Schools stay closed. Cinemas, gyms, theatres etc.. all closed. No travelling. You can go to the shops but have to stay a metre away from others. Today I queued up outside the supermarket (a metre between each person) and there were only about 10 people in at a time. When one person left, one went in.

 

[LDC]

Does anyone have a good summary of what lockdown looks like in Italy?
What are the rules?

Someone I know there is doing good informative posts about this. I'll try and get one and stick it up here.

 

[ska invita]

Someone I know there is doing good informative posts about this. I'll try and get one and stick it up here.

Cheers, I'd really like to see the detail.

 

[PD58]

Graph of the daily increase from your figures (assuming my additions are right). Averaging out looks exponential to me, particularly given the last few days.

You keep stressing exponential needs to be doubling every day - it really doesn't.

No i don't, read my post...exponential means it is increasing at a constant rate (I say double as that is what it did start at) and this isn't - i have never said that it is not increasing quickly but it is not exponential as some days the increase is greater than or less than the day before (both absolute and relative) which is to be expected and in fact 8 March is an outlier given what has come before. If it was exponential you should be able to predict what the next day is...

RE sptme start with 12 then to 26 is 2.16, so next period is 56 which is what we have but then it should be 121 but is 156 so this is not exponential...it is actually faster., the next period is also faster but then it looks like it might be slower.

If anyone is that interested in how diseases might spread search logiistc growth model and considerable research indicates across a range of diseases that growth (not deaths) is generally sub exponential...

On the plus side it does seem toe b levelling off in boih China and S Korea, it will be very intereting to see what happnes in Italy and then we are in to the much more interesting discussion about 'democratic' versus 'communist' response

 

[maomao]

For reported disease cases to match an exact pattern of growth expected from a mathematical model of disease transmission you would need to be sure you were testing all the right people. Which we're not.

 

[LDC]

Deputy CMO just announced the UK epidemic peak is likely to start in about 2 weeks.

 

[Flavour]

Does anyone have a good summary of what lockdown looks like in Italy?
What are the rules?

you're not supposed to leave your house except to go to work, hospital or to buy food. all transport between regions and provinces is not allowed except for valid reason i.e. for work, to go home from being away. all cinemas, pubs, clubs, theatres, gyms, leisure centers and any other place of public congregation closed. coffee shops and restaurants must close at 6pm (i.e. no restaurant dinner service anywhere in italy) - basically everything is closed except shops selling food and stuff. obviously the cops can't really control everywhere at once but there are heavy fines and potentially jail time for people who break the rules of this curfew. it's very hardcore indeed.

 

[ska invita]

Deputy CMO just announced the UK epidemic peak is likely to start in about 2 weeks.

Saw that. What does peak mean in this case? Surely not that cases will go down after that two week period

 

[Steel Icarus]

Saw that. What does peak mean in this case? Surely not that cases will go down after that two week period

No. It's when shit goes really bad for a while.

 

[8ball]

It will only spread infection. What looks overdoing now will appear common sense 3 weeks down the line, that's exponential growth and respiratory infection. I'd urge its cancellation.

I'm also working on an event for last weekend of March. Trying to convince the team what the numbers now are actually likely to mean. Got people coming from all over the world (a lot of cancellations so far tbf).

 

[sihhi]

I'm also working on an event for last weekend of March. Trying to convince the team what the numbers now are actually likely to mean. Got people coming from all over the world (a lot of cancellations so far tbf).

Honestly the numbers now will seem like a puddle compared to the torrents later.