Where is COVID-19 heading in Australia?

Update: 18 April 2020, p.m.

The relatively slow decline in active Australian cases (see original post below) reflects some regional variation in the progression of the epidemic. For example, the number of active cases has increased in Tasmania. In Victoria, active cases have declined much faster than the national aggregate. If you head over to Ben Phillip’s COVID-19 forecaster and select Victoria, you will see that the number of cases has been halving ever 4-5 days. One gets a similar rate of decline if examining the number of new cases in Victoria when excluding imports (both new cases and the number of active cases should decline exponentially).

BenFlipsVic

Number of active cases in Victoria with a fitted exponential curve (from au.covid19forecast.science.unimelb.edu.au). This rate of decline is substantially faster than for the aggregated Australian data.

With that trend, the expected number of active cases in Victoria will equal 0.5 by mid May. That is a little more encouraging than when examining the aggregated Australian data. The data for New South Wales is unreliable because the number of recoveries has not been updated consistently over time in the JHU data repository. However, rates of decline in some other Australian states and territories have been similar to Victoria (e.g., the number of active cases have halved in less than a week in the ACT and South Australia).

Original post

In Australia and a few other countries*, COVID-19 cases are declining. But where are we heading? Here I look at the data to answer that question.

In one of my previous posts, I mentioned that typical epidemiological model predict exponential growth in the early phases of an epidemic (in the absence of further importation of new cases and if the transmission rate remains constant). The previous posts aimed to investigate the degree to which transmission rates were changing in Australia (and elsewhere) as control measures were implemented.

Now that Australia has a relatively stable (and low) rate of transmission, we still expect the number of active cases to change exponentially but now it will be exponential decline because physical distancing is helping to control transmission of coronavirus.

When cases increase exponentially, the rate of increase gets faster with time. In contrast, the rate of decline gets slower with time under exponential decline. Over the last week or so, the number of active cases in Australia has declined at a rate of about 15% per week. That is, the number of active cases now is about 85% of the number that existed one week ago.

If that rate of decline continues, then in two weeks we would expect the number of cases to decline to 85% × 85% = 73% of the number now. Over another two weeks (four weeks in total), we would expect the number of active cases to decline to 53% of the number now (85% × 85% × 85% × 85%). You will note how the rate of decline gets slower and slower.

DiffRValues

Change in the number of cases when increasing exponentially at a rate of 15% per week (red), and when decreasing exponentially at 15% per week (blue). Increases accelerate, while decreases decelerate with exponential dynamics.

 

It takes about 19 weeks (almost 4.5 months – i.e., late August) to get the number of active cases to one twentieth of the number now with a decline rate of 15% per week. We currently have about 2600 cases in Australia, so this projection would suggest we will have about 130 cases by late August. That is approximately the number of cases that existed a little over a month ago.

This might seem a little disheartening. The increase in occurrence that we have seen in the virus in about a month (even with effective physical distancing for much of that time) will take almost 5 months to eliminate. This emphasises the difficulties faced when managing coronavirus in Australia.

Of course, we don’t have much data to estimate the long-term rate of decline in the number of active cases; the number of active cases in Australia has only been declining for a couple of weeks, so our estimate of the rate of decline is uncertain. It is possible the incidence of COVID-19 cases might decline faster than 15% per week. Or cases might decline less quickly.

Nevertheless, this analysis suggests to me (and as foreshadowed by the Federal and State Governments of Australia), that management of coronavirus in Australia (and elsewhere) is a long-term proposition.

*very few other countries.

About Michael McCarthy

I conduct research on environmental decision making and quantitative ecology. My teaching is mainly at post-grad level at The University of Melbourne.
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