Piet Streicher PhD Engineering
As this post reaches its fourth revision, it is becoming increasingly information-dense, based on criticism received from, amongst others, Dr Harry Moultrie of the National Institute for Communicable Diseases (who remains fiercely critical).
There are strong indications that daily new Covid-19 cases in the Western Cape are not increasing exponentially anymore. Hospitalisations, ICU beds and deaths are all starting to fall behind what used to be a very consistent 8% growth per day. Based on the experience of most countries worldwide this slowdown is to be expected. Within the next few days the certainty of a slowdown is likely to become unquestionable. The implication of a slowdown now would be an irrefutable confirmation that the official Covid-19 models for South Africa grossly overestimated the peak for the Western Cape and for the rest of the country. Decisions based on these models would then need immediate revision.
The analysis and interpretation of the data is complicated by a growing backlog in tests, the cessation of community screening and testing (CST) and constraints on ICU staff available. My analysis is based on the information provided by the government. I make several observations and provide my best attempt to interpret this data. I make five arguments in support of my hypothesis that the rate of increase in Covid-19 cases is slowing down. No single argument is conclusive, however looking at all five arguments as a whole I conclude that there are strong signs that my hypothesis is correct.
By making this analysis available in the public domain, the intention is to improve our collective understanding of the problem. I welcome arguments against my hypothesis.
Most countries slow down earlier than expected
Almost all countries change from exponential growth to a more linear pattern much earlier than originally predicted. Figure 1 shows the worst 25 countries (of 10 million people or more). The blue line is for Belgium which exhibited this change on day 25 at which point 160 new cases per 1 million people were recorded. The level at which this change occurs appears to be independent to the level of lockdown measures employed.
Figure 1: Belgium new confirmed Covid-19 cases per day normalized by population (source: 91-divoc.com)
On a regional basis, this turning point might happen at a higher level, but still well below original predictions used in the official SA Covid-19 models. Figure 2 shows the same information for all states in the USA. The blue line is for New York State which exhibited this change between day 16 and 35 at which point (day 35) 551 new cases per 1 million people were recorded.
Figure 2: New York State new confirmed Covid-19 cases per day normalized by population (source: 91-divoc.com)
The Western Cape is expected to slow down
The Western Cape has a population of 5.8 million people. 921 confirmed new cases as on May 16 equates to 159 new cases per million people per day. This is a level where we can expect a slowdown.
Argument 1 – Confirmed Covid-19 cases by date of test result are not growing exponentially anymore
Figure 3: Western Cape new daily confirmed Covid-19 cases.
Looking at Figure 3 there appears to be a slowdown after May 19. A growth projection of 8% per day which the Western Cape has consistently followed from May 1 to May 18 would have projected an average of 1 836 new cases for the last 3 days of May. The actual average for the last 3 days of May were 1 272.
The counter argument to this observation is that trends in confirmed cases do not always correspond to trends in actual cases and this could be caused by a testing backlog or by the cessation in community screening and tests (CST). A testing backlog is likely to build up gradually and would not explain the change around May 19. This hypothesis is confirmed by my next argument.
Argument 2 – Number of confirmed cases plotted by date of sample taken is not growing exponentially anymore
Figure 4: Western Cape confirmed cases by both sample date and by date of completion.
Figure 4 shows the confirmed cases by date of sample (green and orange lines). The move away from exponential growth on May 15 is clearly evident and the updates to this data received on May 31 did not change the trend already observed on May 27. The data also indicates that the average time from sample taken to test completion is around 5 days. While the green line might move up marginally over the next day or two, the slope of the green line is unlikely to change.
Argument 3 – Daily new tests completed are not increasing exponentially
Figure 5: New tests completed each day.
Another indication of a possible slowdown could include a slowdown in tests done, as this might be driven by the number of people that present symptoms. However, testing capacity constraints would also lead to a slowdown in tests done and this might result in the finding of less active cases. There are testing capacity constraints and this has resulted in a significant reduction in CST tests. Note however that CST testing made up less than 17% of all testing at the peak according to the Western Cape Department of Health. Testing continues to increase, although not at the same rate as new cases. As tests are rationed, we can expect the test positive percentage to increase as tests are limited to only those that clearly show Covid-19 like symptoms. We see this increase countrywide, except in the Western Cape.
Argument 4 – The test positive % over total tests stopped increasing exponentially
Figure 6: Confirmed cases as a percentage of new tests completed each day.
The confirmed cases as a percentage of tests done increased very consistently at 8% per day up until May 19 after which this trend stopped (figure 6). This is another strong indication of a slowdown and this metric can be used even when there is a testing capacity constraint.
Argument 5 – ICU beds occupied and deaths have stopped growing exponentially
Figure 7: ICU beds and deaths
ICU beds occupied stopped growing exponentially on May 22 and has grown marginally at 3-4 beds per day since. There are staff constraints in terms of ICU beds that could explain a portion of this trend.
If this trend is an indication of a reduction in the rate of increase in the demand for ICU beds, we can expect a change in deaths from exponential to linear growth 9 days later. While deaths have tracked the 8% a day projection almost exactly for more than 21 days already, by the 31st where we expected to see 38 deaths, only 16 were recorded. At this stage it is only one data point, but this aspect will be tracked closely in the following days.
SA Covid-19 Modelling Consortium predictions
The South African COVID-19 Modelling Consortium is group of researchers from academic, non-profit, and government institutions across South Africa. The group is coordinated by the National Institute for Communicable Diseases, on behalf of the National Department of Health. This group published a report on 6 May titled: Estimating cases for COVID-19 in South Africa, Long-term provincial projections.
Figure 8: Western Cape projections from the official SA Covid-19 consortium model.
Before discussing the predictions made by the consortium it is important to understand some definitions:
Symptomatic cases: those with Covid-19 that exhibit symptoms whether mild or severe and include those tested positive and those not tested.
Confirmed cases: those that have tested positive for Covid-19.
The consortium stated that all hospitalised and severe cases will be tested but only 1 in 4 mildly symptomatic cases will be tested. Since less than 10% of confirmed cases are hospitalised in SA, we can approximate confirmed cases as 1/4 of symptomatic cases.
Unfortunately the consortium does not show projections for confirmed cases, even though the data released every day by the NICD and by the entire world refers to confirmed cases. This causes unnecessary confusion amongst the general public. It is absolutely critical that projected numbers for confirmed cases are also shown, as then everyone will be able to compare the model to the daily numbers released by the NICD.
The consortium published a model of symptomatic active Covid-19 cases per province over the next 9 months. It peaks at 100 000 – 220 000 symptomatic active Covid-19 cases for the Western Cape (Figure 8). This translates to 25 000 – 55 000 active confirmed cases for the Western Cape. This is slightly over double my prediction of 10 000 – 20 000 active confirmed cases. To put this in perspective, 25 000 – 55 000 active confirmed cases for the Western Cape would be 4 300 – 9 500 active cases per million people. This will be worse than Belgium (2 900), UK (3600) or the USA (3800), which are the three worst countries in the world ito of this number. It will be better than New York State (14000), the worst region in the world ito this number.
The consortium reports that for 100 000 – 220 000 symptomatic active cases (25 000 – 55 000 confirmed active cases), the Western Cape would need 8 000-17 500 hospital beds and 3 000 – 6 000 ICU beds.
This is a ratio of 9 : 4 : 1 for active confirmed : total hospital beds : ICU beds.
Currently the Western Cape exhibits a ratio of 35 : 4 : 1 . (Note that ICU beds occupied today relate to active confirmed cases 1-2 weeks ago).
Is it possible that the consortium made a mistake in conflating symptomatic with confirmed cases? Did they apply a ratio of 35 : 4 : 1 to the 100 000 – 220 000 active symptomatic cases instead of applying this ratio to the 25 000 – 55 000 active confirmed cases?
A more realistic projection for all hospitals in the Western Cape will be the following:
A maximum of 10 000 to 20 000 active confirmed cases in the entire Western Cape (on 31/5 it was at 10 004).
900 – 1500 in hospital 1-2 weeks after reaching peak infection rate
300 – 600 in ICU 2-3 weeks after reaching the peak infection rate
* 900 – 1 300 total deaths from Covid-19 in the Western Cape from April to September.
* 6/6 revision – the estimate is now 2 000 – 4 000 deaths for the Western Cape.
* 12/6 revision – 3500-5000 deaths (see next article).
These predictions are in line with predictions independently made by Pandemic Data and Analytics (Panda), a multidisciplinary initiative co-ordinated by actuary Nick Hudson.
Indications from new daily confirmed Covid-19 cases by test completion date, cases by test sample date, positive tests as a percentage of daily tests completed and ICU beds occupied all indicate that the rate of increase in new Covid-19 infections in the Western Cape is starting to slow down. Confirmed cases by sample date stopped growing exponentially on May 16, ICU beds stopped growing exponentially on May 22 (6 days later) and deaths stopped growing exponentially on May 31 (15 days later). Based on the experience of most countries worldwide this slowdown is to be expected. It is becoming very clear now that the official Covid-19 models for South Africa grossly overestimated the peak for the Western Cape. Decisions based on these models need urgent revision.
For more regular updates on how this data unfolds, follow: http://www.facebook.com/masksforallsa/
My calculations and assumptions may contain errors. The purpose of the article is to make a contribution in addressing the pandemic. I hope my analysis will aid the various Covid-19 modelling teams, the journalists that track the problem, the politicians that have to make very difficult decisions and the general public. If an error is spotted, please comment on the article and I will correct it. Note that a slowdown in the rate of increase in confirmed Covid-19 cases is not an indication that Covid-19 should not be taken seriously.
I would like to acknowledge the input provided by the following organisations and individuals:
Various members of Pandemic Data and Analytics (Panda) provided invaluable input. Panda is a multidisciplinary initiative co-ordinated by actuary Nick Hudson.
Critical input was provided by Dr. Harry Moultrie NICD (who remains fiercely critical).
The Western Cape Department of Health answered multiple questions around testing processes, testing constraints and ICU staffing constraints.
Acknowledging all these parties is no indication that my analysis is supported by them, in fact the last two remain fiercely critical.
SA Covid-19 Modelling Consortium report from 6 May:
Estimating cases for Covid-19 in South Africa – Long-term provincial projections. Report Update: 6 May 2020. Prepared by MASHA, HE2RO and SACEMA on behalf of the South African COVID-19 Modelling Consortium
Nick Hudson et al, 2020. The mortality and economic effects of Covid-19: Datasets for decision making. Published in Terry Bell, May 5, 2020. Actuaries warn Ramaphosa of a ‘humanitarian disaster to dwarf Covid-19′ if restrictive lockdown is not lifted. Daily Maverick.
27/5 update: The R0-number is dropping consistently for the Western Cape and is down to 1.13. R0 is calculated by taking the average confirmed active cases over the last 7 days and dividing this by the average active cases over the last 14 days. If R drops below 1.0, the active cases reached a turning point 7 days previously.
Figure 9: R0-number for Western Cape
Table 1: Western Cape projections and actual data (own analysis).