SCARCS Calendar:
Today is Thursday, 20200402
In Part I, I built an exponential model using data between March 2 and March 15, then continued to add daily numbers to see how that model tracked:
Initially, the number of cases doubled every 2.7 days, predicting almost 1600 cases by the end of Saturday March 21, but since Thursday, the infection rate seems to have slowed down a bit and we got about 1331 cases instead. This deviation from the exponential model is what I explore below.
There's a ratio involving three data points that's useful to track how “fast” the exponential grows. It's easier to explain with an example, so suppose we had three days like this:
Day  # of Cases  New Cases  Growth Factor 

Day1  100  
Day2  110  10  
Day3  130  20  2 
To calculate the growth factor:
Here are the number of cases in Canada with the calculated growth factors:
Date  # of Cases  New Cases  Growth Factor 

20200301  ?  
20200302  27  
20200303  27  0  
20200304  33  6  
20200305  37  4  0.67 
20200306  48  11  2.75 
20200307  60  12  1.09 
20200308  64  4  0.33 
20200309  77  14  3.25 
20200310  95  18  1.38 
20200311  117  22  1.22 
20200312  157  40  1.82 
20200313  201  44  1.10 
20200314  254  53  1.20 
20200315  342  88  1.66 
Date  # of Cases  New Cases  Growth Factor 

20200316  441  99  1.33 
20200317  596  155  1.57 
20200318  727  131  0.85 
20200319  873  146  1.11 
20200320  1087  214  1.47 
20200321  1331  244  1.14 
20200322  BC did not report its numbers on March 22.  
20200323  2091  380  1.56 
20200324  2792  701  1.84 
20200325  3409  617  0.88 
20200326  4043  634  1.03 
20200327  4757  714  1.13 
20200328  5655  898  1.26 
20200329  
20200330 
There's a lot of variation in the growth factor because real life is messy. It's also worth keeping in mind that the numbers we see are contingent on how much testing we do. It's easy to imagine that testing labs are lagging a few days behind and that they'll sometimes be able to report more results one day and less the next.
We don't have an accurate picture of the world here so it's hard to make any kind of hard predictions. Nevertheless, as of March 21, there seemed to be a loosely decreasing pattern:
Overall, the growth factor is mostly above 1 (in the exponential phase), but it looks like we might be on track to reach 1 by the end of the month (end of exponential phase). If that's the case, and if we continue to implement measures to slow the down the spread, then we'll be in a better position to estimate the final outcome by the end of the month. Here's why.
In Part I, we saw that very different Logistic Curves can fit the current data, and that there's really no way of knowing which path we're on yet. Here they are again:
Show Formulae
Show Formulae
Logistic 1  Logistic 2  Logistic 3 



Here are a few things to know about the Logistic Curve. In the middle:
So once we reach that point, we'll be able to get a better estimate of where we'll end up. Until then, things are still very much in the air.
A lot happened this week:
Over all, it looks like we are back on the exponential curve with an overall doubling time of 3.1 days:
The Growth Factor also seems to support this as it is barely decreasing.
Over a week ago, back when we only had 342 cases, the model (at the time) predicted we were about two weeks behind Italy (which had 26,000 then).
The updated model (doubling every 3.1 days) predicts that we are about 12 days behind Italy (with now has over 92,000 cases). Whatever we have been doing is either not working or we are not seeing the effects yet.
According to the CBC from March 25th:
“Dix and provincial health officer Dr. Bonnie Henry both said they are optimistic B.C. isn't following the same path as countries like Italy that have seen their healthcare systems overwhelmed by huge spikes in hospitalizations and deaths.”
Countrywide, the numbers disagree. We have about two weeks behind Italy since the beginning of March. Provincewide, the numbers do look better, but it could well be because we are not testing as much as other provinces like Quebec and Ontario. There are no reasons to be optimistic about being on a different path.
Here's a different way to look at the exponential curve when the number of cases is presented as a multiple of 10 on the vertical axis (called a logarithmic scale):
If we stay on that line, we'll reach 100,000 cases by April 10^{th}!
Here's a video shared by the Mid Island Radio Group: