We are in a slow dance with COVID-19

Ontario has decided to face the music, but that doesn’t mean normal will return any time soon

In the classic movie tune by Irving Berlin, romantic partners played by Ginger Rogers and Fred Astaire see “trouble ahead,” but the lure of the “moonlight and music” makes them decide: “Let’s Face the Music and Dance.” What results is one of the best-loved five minutes of the Golden Age of Hollywood.

We also find ourselves in a situation where there may be trouble ahead. The COVID-19 epidemic has peaked, but the way forward is uncertain. With the lure of good weather, thoughts are turning away from the epidemic and toward a more normal life. How will our actions will be remembered in hindsight?

It is wonderful to see the initial climb in the active cases of COVID-19 in Ontario turn around. The active cases are those that are currently infectious, and is given by:

Active cases = Total cumulative cases — Total cumulative recovered — Total cumulative deaths

Using the government of Ontario official numbers, the active cases on each day since March 10 is shown in the top graph. On the 46th day after imposing social distancing limitations, the number of active cases peaked. Our collective effort to stall the epidemic and avoid a crisis in hospitals was a success — a great achievement worth celebrating. Is it now safe to relax restrictions? By how much? For this, we need to look at where the epidemic is headed, not where it is.

Viruses spread exponentially, according to how difficult it is to create new active cases by infection from existing active cases. This is described by the Daily Multiplier (DM):

DM = (Active cases today/Active cases yesterday).

The Daily Multiplier changes when the ease of transmitting the infection changes. This can be seen in the bottom two graphs, where the Daily Multiplier for each day is shown. Look first at Canada’s DM, on the bottom left. At the beginning, the DM is about 1.23. This gives a doubling of active cases every 3 1/2 days; this initial value was found in many countries.

Day 1 on the graph is when social distancing was instituted and created conditions for a lower DM. However, it usually takes two weeks for an active case to become symptomatic, so the DM did not start to change for two weeks. (The vertical lines on the graph mark these two week intervals.) Once the DM began to fall, like an enormous ship that does not respond immediately to a change in rudder setting, it took another two weeks for it to move to the new value of 1.04 (doubling every 18 days). Then new regulations were put place to address the terrible problem in long-term-care residences. This created the conditions for an even lower DM, and two weeks later the official numbers started to show the change. By the 58th day, Canada’s DM seemed constant once again, near one.

Canada’s epidemic is really many localized epidemics in different regions. The Daily Multiplier for Ontario is shown in the graph on the bottom right. For Ontario, the changes in long-term care caused the DM to pass through one on the 46th day, when the peak in active cases occurs. The DM continued to fall and reached as low as 0.93. If it stayed at 0.93, the active cases would halve every nine days, and wipe out the epidemic in three weeks — or would it?

Actually, the future course of the epidemic is not determined by the number of active cases, but by the DM. Any relaxation of current conditions will make transmission of the virus easier and cause the DM to increase. How much can controls be relaxed and still keep the DM less than one? It is difficult to say, and it will take two weeks for any change to begin to show up and another two weeks to settle to a constant value. Four weeks is a long time to be uncertain whether the epidemic is secretly growing. The new normal

How much can controls be relaxed and still keep the DM less than one? It is difficult to say

must have social limitations that keep the DM below one. The delicacy of the balance is indicated by the recent rise of the DM in Ontario, so that the number of active cases hit a plateau and began to rise in the last few days.

Ontario is now proceeding to relax social and commercial restrictions, so it seems we have decided to “face the music.” But unlike Fred Astaire and Ginger Rogers, we will not be free to choose our partner. We are obliged to have a slow and cautious dance with COVID-19 — one tentative step forward and then one back, locked together for a long time yet to come.