Canada continues to steadily move toward flattening the curve, but it has not yet reached that point. Ontario and Quebec continue to contribute about three quarters of newly confirmed cases of COVID-19 per day, and over the last week British Columbia has seen a slight reversal of the gains it has made over the three weeks prior.
Although there are many positive signs, including data showing that five provinces may be able to begin reducing physical distancing measures when a fast and reliable testing method available, Canada has yet to reach the all important point of inflection when we begin to see the curve actually start to flatten.
What does it mean to flatten the curve and how do we know it has actually happened? Conveniently we have a real-world example in South Korea with which to illustrate this challenge.
Above we see the number of confirmed cases in South Korea from February 16th to the March 15th (using a linear scale to emphasize the curve). The shape of this curve is called a Sigmoid, and it can be mathematically described using a Logistic Function. This is the curve that all infectious diseases follow; as more people catch the disease and become infectious themselves they are able to spread it to more people and the total number of cases increases exponentially. However, as the number of unaffected people begins to shrink, the number of new cases begins to fall and the curve starts to flatten. This could be because measures have been put into place to prevent spread, or because everyone has become ill. This is what the term “flatten the curve” refers to.
It is easy to see this shape with the benefit of hindsight, but when you are at the points labelled A or B, with no insight into the future, how do you know whether the curve is flattening to getting steeper?
How steep the curve is at any given point can be determined using the ‘growth ratio’. At its core the growth ratio is calculated by taking the number of new cases today and dividing it by the number of new cases yesterday. If this number is greater than 1.0 that means there were more cases new cases today than yesterday; less than 1.0, fewer. This produces a very noisy signal and it can be tough to identify trends because new case identifications do not conveniently produce a smooth curve.
We can smooth this noisy signal using an averaging function: take the average growth ratio over 7 days – half the period of time that is generally accepted to be where one is potentially pre-symptomatic. However, as shown with the yellow series in the image above for the seven days following the 19th of February, this too can produce odd results when there are component figures that are wildly out of line with the rest of the series.
The solution to this is to weight the components; for the purposes of all charts and analysis in these posts each day back from the current day is de-emphasized by 25%. Below is the specific formula used throughout these analyses. (Remember to make sure that the denominator used is the sum of the weights, or else the result will be off).
The result of using the weighted averaging formula is a smoother curve that also corrects for the occasional wild swings in the data.
The result of all of this is the green line – the same weighted averaged growth ratio used throughout these analyses. Using that green line, at the point labelled A we would have been able to tell right away that the spread of COVID-19 was still not contained in South Korea. However, by the point labelled B we had seen the averaged ratio of growth settle near the 1.0 mark for several days and it had finally dipped beneath it. That too would have been too soon to truly label the B as the point of inflection but at the moment would have been cause for hope. With a few additional days of data, B could definitively be called the inflection point.
While on first glance the situation in British Columbia seems to have stumbled slightly since the report last week the low number of cases overall tends to make for more pronounced jumps in growth ratio changes. Over the last 6 days the average number of new confirmed COVID-19 cases has been 27/day, while the preceding six day period saw an average of 32/day. Should a fast and reliable testing method come online, BC may continue to be a suitable candidate for a relaxing of physical distancing measures.
Growth of newly confirmed cases in the Prairie Provinces cases continues to be dominated by Alberta, which has been responsible for 98% (937 of 959 total) of the new cases in the region in the last six days. Despite that, the rate of growth has started to slow overall, and soon Alberta may be able to join Saskatchewan and Manitoba in the may be suitable category for relaxing physical distancing measures. As always, that suitability is contingent on specific conditions on the ground that are not addressed in these state of the country reports, and on there being fast and reliable testing methods available.
Ontario has struggled in their handling of COVID-19, but there are positive signals. While the averaged number of new confirmed cases is more than 2.5 times what it was 4 weeks ago, the rate of acceleration in growth is lower than it has ever been, even crossing the all important 1.0 mark on two separate days over the last week. Though Ontario may be at the point of inflection – where the curve begins to be flatten – its position is tenuous and the picture presented here may be distorted by widely reported issues around a lack of testing.
Quebec has seen great progress in the handling of their COVID-19 outbreak over the last week, seeing their averaged growth rate fall by 20% and seeing another two day period when their growth rate was below the 1.0 mark. Like with Ontario, Quebec may be at the point of inflection in their logistic curve, though may also have its picture distorted by issues around a lack of testing.
Growth in confirmed cases continues to be dominated by cases confirmed in Nova Scotia, although even when it is included the overall case load continues to be relatively low. In fact, excluding Nova Scotia, the Atlantic Provinces recorded no newly confirmed cases from the 19th to the 21st of April. New Brunswick, Prince Edward Island, and Newfoundland may all be candidates for having physical distancing measures reduced as soon as fast and reliable testing becomes available. Nova Scotia too has seen its averaged growth ratio fall nearly 20% and may soon be a candidate itself for reducing physical distancing measures.
Data used in this post is accessible here.
April 16th analysis accessible here.
Feature Image by Felipe Esquivel Reed; Image obtained from Wikimedia.