Indeed, the plot presented by the government seems to show that lower curves (i.e., with fewer ICU beds at their peak) are wider (i.e., they take longer times to go down to zero). But the plot is misleading. It is an exercise in Statistic gone wild, in which the government's "scientists" have played with the numbers while losing sight of what they mean.
How can fewer cases at any given time prolong the duration of the pandemic? It is pure nonsense that results from blindly accepting the results spewed out by a computer.
For one thing, there is no reason for the curves to be symmetrical. On the contrary, there are reasons for assuming that they will have a "long tail" due to overseas arrivals and probably other channels of re-infections. This is happening in China and South Korea (see below).
In fact, the two halves of the curves are most likely going to be different. See for example what has happened in China and Korea (to prepare my plots, I relied on the data provided by the World Health Organisation in their daily situation reports on COVID-19):
Both coutries experienced a rapid increase of daily new cases, followed by declines thanks to the mitigation actions. Note how neither country has managed to completely squash the number of daily new cases.
The government's plot shows estimates of ICU beds, while my plot shows daily new cases. But, as I explain later in this article, the two numbers are linked to each other. If I had plotted the data for ICU beds in China and Korea, the shape of the curves would have not been substantially different (as long as the ICUs managed to remain below saturation, as that would have cut the top of the curves).
That in the government's plot flatter curves are shown farther away from day zero is meaningless and confusing. What has the shape of the curve to do with when a pandemic begins affecting a country? Please!
As another example of curve asymmetry, let's compare Australia and Korea:
In this plot, the curves show the numbers of new daily cases averaged over one week (three days on either side). To facilitate the comparison of the two curves, I have also removed from the plots the initial days of the infection, in which the numbers of daily new cases in each country were very few (four or less) and sporadic.
I chose Australia and Korea because they reached comparable numbers of maximum daily new cases and both are clearly past the peaks of their respective distributions. Notice how the number of new cases grew in Korea more rapidly than in Australia while the descending sides of the curves are very similar. In any case, contrary to what our government tells us, the curves are far from being symmetrical.
That the government's plot is an exercise in statistics becomes even clearer when you look at the Wikipedia page on the normal distribution:
This must be where the government's overpaid modellers have got their ideas...
Now let's explain how the number of ICU beds and the daily number of new cases are linked.
If we get 1,000 new cases today and 1,000 new cases tomorrow, each group will require a similar number of ICU beds after a week or so.
The current status (2020-04-09 13:45) provided by the Department of Health tells us that in Australia we have a total of 6,013 cases and 87 patients currently in intensive care.
That said, you cannot simply calculate that 1,000 new cases will require more or less 87/6013 = 15 additional ICU beds a week later because to determine the total number of ICU beds needed, we need to take into account for how long each patient remains in ICU: the longer the patient stays, the more beds we need. Furthermore, sadly, we also have to take into account the number of deaths (currently 50 in Australia). Careful modelling is required to prepare reliable projections.
A critical issue in modelling the pandemic is how to estimate future numbers of new infections, especially when considering that some infected people have no symptoms an can therefore spread the virus undetected. The only way to get hold of such community-based transmission is to test lots of people. This is why the WHO's Director has been promoting "testing, testing, testing". Fortunately, our government got it right, relentlessly testing as many people as possible, the only limitation being the number of testers and the availability of test kits. A better knowledge of community-transmitted cases will result in better models.
