Brief analysis of daily UK coronavirus deaths
AG
2020_06_16
Simple views of the data
The data are the daily deaths from Covid-19 in the UK, announced by DHSC each day, and usually available at https://coronavirus.data.gov.uk/archive. The archive was effectively down for two days as of 29th May apparently owing to a coding error, but now seems restored to health. The daily deaths are reported by DHSC each day, and so can be manually added when the archive is unavailable.
This document was prepared using R-markdown and RStudio.
This section has simple tables and figures, the following section uses them to look at how the future may develop, and then the final section employs more formal modelling methods to make predictions about the the remaining deaths in the “first wave”.
Table 1 shows the death tallies arranged by day of the week, and Figure 1 plots them by day of the week. Each curve has a much simpler pattern than if we ignored day of the week. The weekly pattern is presumably due to working shifts and administrative arrangements for people involved in different stages of reporting a death.
## [[1]]
## 6Mar- 13Mar- 20Mar- 27Mar- 3Apr- 10Apr- 17Apr- 24Apr- 1May- 8May-
## 6Friday 1 1 36 284 714 1152 935 1005 739 626
## 7Saturday 1 18 56 294 760 839 1115 843 621 345
## 1Sunday 0 15 35 214 644 686 498 420 315 269
## 2Monday 1 22 74 374 568 744 559 338 288 210
## 3Tuesday 4 16 149 382 1038 1044 1172 909 693 627
## 4Wednesday 0 34 186 670 1034 842 837 795 649 494
## 5Thursday 2 43 183 652 1103 1029 727 674 539 428
##
## [[2]]
## 8May- 15May- 22May- 29May- 5Jun- 12Jun-
## 6Friday 626 384 351 373 357 202
## 7Saturday 345 468 282 226 204 181
## 1Sunday 269 170 441 115 77 36
## 2Monday 210 160 121 111 55 38
## 3Tuesday 627 545 136 324 286 233
## 4Wednesday 494 363 434 359 245
## 5Thursday 428 338 413 176 151Table 1. The numbers of deaths arranged by day of the week
Figure 1. The numbers of deaths plotted by day of the week
Next, in Table 2 and Figure 2, we express each figure as a ratio, by dividing it by the figure of exactly one week previously. These ratios are not affected by day of the week effects, and they also incorporate a whole week of change, so are likely to be more reliable indicators. The obvious pattern is that the ratios are high to begin with, and do get gradually lower. The grey line at a ratio of one separates ratios indicating numbers are increasing, from those that indicate a decrease
## [[1]]
## 13Mar- 20Mar- 27Mar- 3Apr- 10Apr- 17Apr- 24Apr- 1May- 8May- 15May-
## 6Friday 1.00 36.00 7.89 2.51 1.61 0.81 1.07 0.74 0.85 0.61
## 7Saturday 18.00 3.11 5.25 2.59 1.10 1.33 0.76 0.74 0.56 1.36
## 1Sunday Inf 2.33 6.11 3.01 1.07 0.73 0.84 0.75 0.85 0.63
## 2Monday 22.00 3.36 5.05 1.52 1.31 0.75 0.60 0.85 0.73 0.76
## 3Tuesday 4.00 9.31 2.56 2.72 1.01 1.12 0.78 0.76 0.90 0.87
## 4Wednesday Inf 5.47 3.60 1.54 0.81 0.99 0.95 0.82 0.76 0.73
## 5Thursday 21.50 4.26 3.56 1.69 0.93 0.71 0.93 0.80 0.79 0.79
##
## [[2]]
## 15May- 22May- 29May- 5Jun- 12Jun-
## 6Friday 0.61 0.91 1.06 0.96 0.57
## 7Saturday 1.36 0.60 0.80 0.90 0.89
## 1Sunday 0.63 2.59 0.26 0.67 0.47
## 2Monday 0.76 0.76 0.92 0.50 0.69
## 3Tuesday 0.87 0.25 2.38 0.88 0.81
## 4Wednesday 0.73 1.20 0.83 0.68
## 5Thursday 0.79 1.22 0.43 0.86Table 2. The ratio of number of deaths to the preceding same day of the week
## [[1]]
## 20Mar- 27Mar- 3Apr- 10Apr- 17Apr- 24Apr- 1May- 8May- 15May- 22May-
## 6Friday 36.00 284.00 19.83 4.06 1.31 0.87 0.79 0.62 0.52 0.56
## 7Saturday 56.00 16.33 13.57 2.85 1.47 1.00 0.56 0.41 0.75 0.82
## 1Sunday Inf 14.27 18.40 3.21 0.77 0.61 0.63 0.64 0.54 1.64
## 2Monday 74.00 17.00 7.68 1.99 0.98 0.45 0.52 0.62 0.56 0.58
## 3Tuesday 37.25 23.88 6.97 2.73 1.13 0.87 0.59 0.69 0.79 0.22
## 4Wednesday Inf 19.71 5.56 1.26 0.81 0.94 0.78 0.62 0.56 0.88
## 5Thursday 91.50 15.16 6.03 1.58 0.66 0.66 0.74 0.64 0.63 0.96
##
## [[2]]
## 22May- 29May- 5Jun- 12Jun-
## 6Friday 0.56 0.97 1.02 0.54
## 7Saturday 0.82 0.48 0.72 0.80
## 1Sunday 1.64 0.68 0.17 0.31
## 2Monday 0.58 0.69 0.45 0.34
## 3Tuesday 0.22 0.59 2.10 0.72
## 4Wednesday 0.88 0.99 0.56
## 5Thursday 0.96 0.52 0.37Table 2a. The ratio of number of deaths to the preceding same day a whole fortnight ago. This helps to understand bank holiday periods better, as one can look back across the distorted period. A formal method could be devised, but gaining enough data would take some more bank holidays for that – we may well get there.
Figure 2. The ratios plotted against time
How quickly will the death rates fall?
The ratios seem to be currently between 0.7 and 0.9, and we can ask how quickly will the numbers decrease? A transformation of the ratios allows us to see in Table 3 and Figure 3 the number of doublings or halvings per week. In the early days, there were large positive figures, indicating more than two doublings per week, so four times as many people were dying at the end of the week than at the beginning. This was a very steep ascent at the beginning of the epidemic.
Later, the doubling times came down, and did so gradually, and eventually became negative on the 15th April (apart from a small number of rare reversions). Once negative, we can take the signs off, and think of them as the number of halvings in a week. For the figures to drop as fast as they rose, we would need to see the number of halvings per week to rise to more than 2, to match the number of doublings per week of 2. However, the number of halvings hovers around 0.3 to 0.4, suggesting it would take 2.5 to 3 weeks to halve the number of deaths. This clearly indicates a very slow tailing off, certainly compared to the very rapid initial increase.
The slowness of decline must be the result of ineffectiveness in our lockdown. Infectious people are still meeting susceptible people, and passing the infection on. These figures don’t tell us whether these are key workers who use public transport, health workers and hospital patients, care home workers and residents, or people not obeying the lockdown restrictions. Or, indeed, it is possible that non-key workers who are obeying the lockdown restrictions are still not sufficiently protected. I am sure someone connected to SAGE is studying these important questions, with more informative data.
These figures can also be used to note that a delay of one week in imposing the lockdown, at a time when there were two doublings per week, would result in an extension of over four weeks now, to get down to any given level. The more formal modelling predictions in the next section give a numerical estimate of this ratio of upspeed to downspeed. The sharp rise and slow fall makes those early decisions look very important.
## [[1]]
## 13Mar- 20Mar- 27Mar- 3Apr- 10Apr- 17Apr- 24Apr- 1May- 8May- 15May-
## 6Friday 0.000 5.170 2.980 1.330 0.690 -0.301 0.104 -0.444 -0.239 -0.705
## 7Saturday 4.170 1.637 2.392 1.370 0.143 0.410 -0.403 -0.441 -0.848 0.440
## 1Sunday Inf 1.222 2.612 1.589 0.091 -0.462 -0.246 -0.415 -0.228 -0.662
## 2Monday 4.459 1.750 2.337 0.603 0.389 -0.412 -0.726 -0.231 -0.456 -0.392
## 3Tuesday 2.000 3.219 1.358 1.442 0.008 0.167 -0.367 -0.391 -0.144 -0.202
## 4Wednesday Inf 2.452 1.849 0.626 -0.296 -0.009 -0.074 -0.293 -0.394 -0.445
## 5Thursday 4.426 2.089 1.833 0.758 -0.100 -0.501 -0.109 -0.322 -0.333 -0.341
##
## [[2]]
## 15May- 22May- 29May- 5Jun- 12Jun-
## 6Friday -0.705 -0.130 0.088 -0.063 -0.822
## 7Saturday 0.440 -0.731 -0.319 -0.148 -0.173
## 1Sunday -0.662 1.375 -1.939 -0.579 -1.097
## 2Monday -0.392 -0.403 -0.124 -1.013 -0.533
## 3Tuesday -0.202 -2.003 1.252 -0.180 -0.296
## 4Wednesday -0.445 0.258 -0.274 -0.551
## 5Thursday -0.341 0.289 -1.231 -0.221Table 3. The doublings/halvings per week, based on the ratios in Table 2. It is the number of doublings in a week if positive, and the number of halvings in a week if negative.