Donate to Remove ads

Got a credit card? use our Credit Card & Finance Calculators

Thanks to uspaul666,WrongLicence388,CryptoPlankton,Anonymous,Instep, for Donating to support the site

Coronavirus - modelling aspects only please

Scientific discovery and discussion
scotia
Lemon Quarter
Posts: 2608
Joined: November 4th, 2016, 8:43 pm
Has thanked: 1144 times
Been thanked: 1149 times

Re: Coronavirus - modelling aspects only please

#358616

Postby scotia » November 20th, 2020, 11:10 pm

Another weeks data on Covid-19 deaths in England - and there's room for optimism, albeit not quite as strong optimism as it may have seemed earlier in the week - if you had ignored the statistical accuracy of the data.

Image

To recap - back on the 5th November I plotted curves which attempted to model the effect of the government's new lockdown on the Death rate in England due to Covid-19. I proposed a simple model. In the Initial period the rate would not be affected by the new restrictions, due to the lag between infection and death. So in this period, a simple growing exponential would suffice. In the final period the lockdown would be fully effective, and a falling exponential would suffice. The in-between period would be an exponential with growth rate varying linearly between the initial and final rates. I plotted three graphs - optimistic, pessimistic and realistic? But I was well out on my estimate of the initial growth rate - it seems to have slowed down considerably over the past few weeks - even before lockdown. So I have left only my most optimistic (green curve) on display.
I have also displayed the reported death rate data on the display. This is significantly day-of-the-week biased, so each data point is a seven day average, plotted at its centre day. I.E. the last data point plotted at the 17th Nov is the sum of deaths reported between 14th and 20th Nov. The vertical bars are the standard deviations, assuming a Poisson distribution.
So based on this reported data, I have plotted a new (grey) curve. This has a lower initial growth rate than I initially used. I still retain the halving time of 14 days which was my original "realistic" value for the final period, but I have extended the middle period - effectively increasing the scatter of days between infection and death. I make no claim as to the accuracy of the prediction, but it probably provides a useful ballpark figure.
Before the end of the month, there will need to be a political decision as to what should happen next. Looking at the grey curve, the death rate at that stage would be similar to that at the start of the month - and I can already hear the cries that lockdown doesn't work - which does, of course, completely ignore the increase if no action had been taken.

scotia
Lemon Quarter
Posts: 2608
Joined: November 4th, 2016, 8:43 pm
Has thanked: 1144 times
Been thanked: 1149 times

Re: Coronavirus - modelling aspects only please

#359126

Postby scotia » November 23rd, 2020, 12:25 am

I have plotted below the past two months data for England - both hospital admissions (green points) and deaths (blue points). Each point is a summation of the preceding week's data. Both sets of points are normalised to unity at their first point. The size of the vertical bars on the points are the statistical standard deviation (for a Poisson distribution). It appears that the admissions may have peaked, but the statistical accuracy of the deaths data can only imply that this rate may be moderating.

Image

It seems probable that the death rate will follow the admissions rate - with a time lag. Assuming that ratio of the death rate to the admissions rate (suitably time lagged) should be near constant, this provides a means of determining the lag. After carrying out a number of trials on the data, I concluded that a delay of 13 days (plus or minus a few days) gave a plausible result. The black points are this delayed ratio. The black lines are displayed to indicate the scale. It seems to be currently running around 0.27. I appreciate that not all of the Covid-19 deaths will be preceded by a hospital admission, but I still find this ratio considerably higher than I expected. Now - a prediction. IF the 13 day lag, and the 0.27 ratio are reasonable values, then moving onwards to the week ending 1st December, the weekly Covid-19 death total in England will be 2855 with a statistical standard deviation of 53, and it will have peaked a few days earlier at 2920 with a statistical standard deviation of 54. This forecast is a bit more gloomy than my 3-part varying exponential model as displayed previously.

Lootman
Lemon Half
Posts: 8320
Joined: November 4th, 2016, 3:58 pm
Has thanked: 74 times
Been thanked: 1469 times

Re: Coronavirus - modelling aspects only please

#359130

Postby Lootman » November 23rd, 2020, 12:37 am

scotia wrote:It seems probable that the death rate will follow the admissions rate - with a time lag.

Doesn't that assume both that we are not getting better at treating this and that general immunity is not increasing?

johnhemming
Lemon Quarter
Posts: 3957
Joined: November 8th, 2016, 7:13 pm
Has thanked: 9 times
Been thanked: 453 times

Re: Coronavirus - modelling aspects only please

#359149

Postby johnhemming » November 23rd, 2020, 4:24 am

Lootman wrote:
scotia wrote:It seems probable that the death rate will follow the admissions rate - with a time lag.

Doesn't that assume both that we are not getting better at treating this and that general immunity is not increasing?

The fact that people are getting more immune would have no effect. In a sense the chart demonstrates that there is no rapid improvement in treatment. It also demonstrates that 13 days is a good figure to pick.

It may be that there was an improvement previously in the year, but not in this period.

The conclusion of a probable peak death rate of just over 400 per day is probably right.

Thank you to scotia for what is a good piece of work that I have not seen done by anyone else.


Return to “Science”

Who is online

Users browsing this forum: No registered users and 1 guest