Ed: I took some flack on the internet because it is statistically impossible for 100% of the population to be infected. While I disagree, my intention with the article was to show a WHAT-IF, not a certainty. Also, it is highly likely that we might indeed reach such high numbers as South African’s see to disregard the lockdown. See my next post on that.
[Errata: These slides show the figures associated with the low road i.e. -20% infection rate as described below. The figures in the text are correct]
Pre-amble
Tonight, at midnight, South Africa enters a window in history never entered before. The country in total lockdown. Never before was a threat to our national security so severe that the whole country was ordered by law to stay at home.
The charts above show, at this rate, we will infect the whole population by 6 May 2020, killing 2.3 million South Africans in the weeks and months to come.
The Corona Virus Disease (Code name COVID-19) caused by the SARS-CoV-2 virus is the driving force behind this harsh intervention.
As an avid strategist, I could no longer sit and wonder how the spread of COVID-19 would occur in South Africa. Over the weekend, 21-22 March 2020, I started to put together a forecasting model to predict how the virus would spread. As the director of the WHO suggested, one’s worst enemy in times like these is perfection. In that spirit, my model is far from perfect or as robust as I would want it to be and yet over the last five days the accuracy with which it predicted our infection rates gave me a degree of comfort that it is good enough to assign some trust.
Methodology
Given that South Africa’s first infection was 5 March, by the 22 there was a substantial amount enough to derive an exponential curve that fitted the rate of infection. In fact, my methodology is actually to establish the CURRENT exponential curve. From there I derive a rate of change (between the previous three day’s of infections or the previous three curves). I then apply this rate of change in perpetuity in three Scenarios:
Current = The current rate of infection less a diminishing factor (ever the optimist that I am)
Current -20% = Simply takes the current rate and only add 80% of the rate of increase to the curve for consecutive days
Current +20% = The same as above except I add 120% of the rate of change
In all three cases, I add a fixed diminishing factor i.e. assuming the rate of infection will slow-down from this point onward. There are two reasons for this. One, I am an optimist and want to believe that all the efforts by the government and every individual will yield some success in slowing the infection rated won. Two, if I did not slow it (in the early versions this week), it was simply too scary. South Africa’s whole population was infected by mid-April with over 2.2Million South Africans dead when all is done. An unthinkable prospect.
Incidentally, some facts, China’s rate of infection only slowed down between 21-23 days after their first lockdown. With our lockdown due to start tonight, we can only expect matters to get worse – much worse before it will get better.
I make some assumptions (in the state of imperfection) and will refine this over time:
- The average lag between infection and symptoms is 5-6 days (with the range varying from 1 to 14 days in reality). Source: https://ourworldindata.org/coronavirus
- It takes 14 days to recover from the virus (with some cases lasting much longer)
- I assume the current global mortality rate will apply to South Africa (and update that daily). This is contentious as Italy has a mortality rate (12%+)much higher than the average (and pushes the average up considerably) while Germany has a mortality rate of below 1%. I will monitor and update this as time goes on.
- Death rate and the lag is very contentious and yet the best I could find is that 11 days after symptoms, is the average where patients will die (I will continue to refine this). Here I introduce a bit of randomness with every day’s delay being the chosen 11 + or – 7 days.
What I do is this:
- Predict the infection rate (as described above)
- Derive New infections by subtracting yesterday’s TOTAL infection from today’s TOTAL infections. I do this for all three scenarios (Current -, Current and Current +)
- From New infections, I apply the mortality rate with a delay (from the assumptions above) to establish fatalities (11 days after new infection) as well as cures, which is the reciprocal figure.
From here on, I will attempt to update the figures daily with some commentary where and if necessary. For the record, according to my model, we should expect our first death any day now. Let’s hope my model is wrong
The bad news
The bad news is that since Monday 23 March, my model has consistently underpredicted our infection rate. All that means is that we continue to adapt an every more aggressive exponential curve. Don’t be fooled by the numbers. Unless you truly understand what an exponential curve is and how it works, the numbers deceive you rather easily (even when you do, it does). It is only by looking at the rate of change that one can establish whether we are slowing down or not.
Think of it like this. If you pull away in a Lamborghini the first few seconds is the fastest acceleration you will ever get and yet, you are still only touching 100km/h, which is not that fast. From then on, you still accelerate, but the rate of acceleration slows down until you reach top speed. While the speed continues to climb, the rate of acceleration is diminishing.
Our bad news is that we are still accelerating and for my money, we are still only at about 10-15 km/h heading for an ugly top speed.
I hope sincerely that my predictions are wrong.
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