Update 2 April (latest graphs):
USA remains a major worry. There are good signs in Australia but more improvement is needed. Spain is better than it was, but still a worry.
You must be tired of exponential trajectories of COVID-19 by now. Well, this blog post isn’t about that directly, but it addresses the same topic – the trajectory of COVID-19. But I hope this is a little more useful for illustrating progress (or lack thereof) in managing the epidemic in each country.
The exponential trajectory of the number of cases is useful as a point of comparison. It shows what would happen in the early stages of a COVID-19 epidemic with only local transmission at a constant rate per infected person (ignoring importation, no controls on spread, and with even mixing of people in a population). We could compare an observed trajectory with that, and hope to see the “curve flattening”. This is the basis of Ben Phillips’ “coronavirus forecaster“.
However, spotting small bends in exponential curves is difficult to do by eye – is that ever-increasing curve starting to flatten? Further, the data that typically get plotted are the number of existing cases, the growth of which includes new cases minus recoveries.
A useful approach is to examine the new cases each day. For COVID-19, the number of local transmissions should be proportional to the number of infected people (in the early stages of the epidemic, when the vast majority of people are still susceptible). It is this proportionality that leads to the expected exponential growth (when the ratio of new to infected cases remains constant).
Further, given an incubation period of five days (roughly that of COVID-19), the number of new cases should be proportional to the number of cases that existed five days ago. In this situation, the ratio of new cases to existing cases from five days ago is the key parameter. I will call this ratio the “rate of new cases”. If we look at that rate, you can get a better picture of the trajectory of the epidemic.
In an epidemic, there will be new cases each day until the disease is almost eradicated. Progress in controlling the disease will be seen by reducing the number of new cases until they are fewer than the number of recovering cases. Therefore, a useful benchmark for assessing new cases is the number of recovering cases per day. To make the number of recovering cases comparable to new cases, we should also scale recoveries by the same factor – the number of existing cases from five days ago.
So, what do these figures look like for some countries?
Australia’s rate of new cases (per existing case) reduced noticeably around 25 March. But more work needs to be done to get the rate of new cases below the rate of recoveries. In South Korea, for example, where the number of existing cases is declining, the rate of new cases is below 0.05. Australia is a long way from that at the moment.
A reduced rate of new cases will arise from changes in behaviour of people and control of importation through measures such as physical distancing and quarantining recent arrivals. Responses in the data will lag these initiatives, with the lag corresponding to the incubation period (about 5 days for COVID-19) plus the time it takes to process tests (which varies from less than a day to several days).
Progressively more aggressive approaches to controlling importation and spread of COVID-19 commenced in Australia from 15 March. It seems likely that the reduction in the rate of infection around 25 March reflects those actions.
The USA is in a worse position than Australia. While the rate of new cases has declined, it remains much higher than the recovery rate, and much higher than Australia’s rate. This suggests the epidemic in the USA will continue to worsen for some time yet.
The situation in Spain has improved, but it is still bad. The rate of new infections has dipped to be similar to Australia, but with many more existing cases, the number of new cases per day remains extremely high (and much higher than in Australia).
This analysis has a few idiosyncrasies. Ideally it would distinguish between local transmissions and importation – the former is much more of a worry if importation can be controlled. However, the daily data I used (from the Wikipedia pages of each country, in case you are interested) only publishes total cases.
Secondly, the analysis doesn’t account for undetected cases. If the proportion of undetected cases remains constant, then this isn’t a problem when calculating the rates (the detection rates cancel when dividing). However, the spike in rates in the USA up until 20 March most likely reflects an increased rate of detection of cases through increased testing rather than an increase in transmission.
So this tells us the USA has hard times ahead, and further limits to transmission seem required to control the epidemic. The rate of infection in Spain and Australia has declined, and it will be interesting to see the extent to which these rates decline further in response to the measures put in place by governments (and hopefully followed by their citizens – people, it’s not time to go to the beach!!!)
But in all three countries examined, the trajectory of the epidemic is clearly still increasing. Please stay at home as much as possible.
Edit: I also did a separate analysis for California and NY State. The big increase in the rate of new infection in NY State is probably a testing artifact. Rates in both states need to reduce substantially.