As governments worldwide respond to the coronavirus pandemic, statisticians and public health experts have been asked to make projections. Making projections of the future is difficult. Apart from the messy relationship between politics and statistics, the future is sensitive to assumptions. This is especially true when one tries to predict exponential growth scenarios such as contagion. Some models, such as the one referenced by Angela Merkel, predict worse-case scenarios of more than 50% infection levels of national populations. Similar predictions have been made in the U.S. Congress and U.K. Parliament. While explosive growth is possible, it is worth exploring existing worldwide data made available by the World Health Organization. WHO data suggests that COVID-19 rages for several weeks within a national population and then dissipates.
Like all statistical projections of the future, there are number of challenges associated with projecting COVID-19 contagion. Before addressing the objections, consider first the available data on China, South Korea, and Iran — three countries hit relatively early by the virus.
The Past: China, South Korea, and Iran
While the reports are disputed, it seems likely that China experienced its first case of COVID-19 late in November 2019, and by the last week of January, the number of its cases reached 1,000. Within a week, the number of cases reached approximately 11,790. For the next ten days, that number grew to about 45,000. During this 10-day period, the average daily growth rate in total cases in China was 20%
After that, the daily growth rate steadily declined (apart from a spike due to additional counting of clinical diagnoses). By the end of February, the daily growth rate petered out to less than 1%. In China, there were two weeks of steady, bulky growth followed by consistent decline.
South Korea experienced a similar pattern of growth and decay. Its first case of COVID-19 was announced on January 20th. The country reached nearly 1,000 cases about a month later on February 25th. For the next ten days, the number of cases grew to about 6,590. During this period the average daily growth rate in South Korea was 20%. Following this 10-day period, the daily growth rate has been steadily declining. As of March 15th, it sits at less than 1%.
Iran reached 1,000 cases on March 2nd. Its average daily growth in cases over the next 10 days was a bit higher than China’s and South Korea’s. Iran averaged 25.82%. But that rate is slowing. The daily growth in cases over the past few days has been between 10% and 12%. Yesterday, March 15th, Iran encouragingly dipped below 10%. If Iran follows a similar pattern to China and South Korea, the number of its new cases should begin to seriously decline over the next 10 days.
The Future: Italy, France, and the United States
Italy, where the virus is currently raging, reached its 1,000th case on February 29th. Italy’s average daily growth in new cases over the next 10 days was slightly higher than Iran’s at 26.54%. While Italy is still hovering around the 20% mark after two weeks like China, it has shown some signs of decline since March 10. If consistent with the broader pattern seen in China, South Korea, and Iran, then Italy should experience a decline in its daily average growth rate very soon, followed by two weeks of further decay. By the end of March or beginning of April, Italy’s daily average growth rate in new cases could fall to less than 1%.
In terms of timing, France lags slightly behind Italy by about a week. It reached its 1,000th case on March 8th. Within the past seven days, the average daily growth rate in France has been 24.31%, slightly lower than Iran. If consistent with the other countries mentioned above, then the daily growth in new cases in France should persist around the 20% mark for another three to eight days, reaching about 10,000 to 12,000 cases by March 19th or 20th if it follows The South Korea Model, or about 40,000 cases by March 26th if it follows The China Model. After either scenario, the daily growth rate should begin to steadily decline and reach less than 1% during the middle of April.
The United States reached 1,000 cases just three days after France on March 11th. Assuming a 25% average daily growth rate, the United States would reach approximately 14,000 cases by March 21st. If the growth were to persist an additional week, like it did in China, then total cases would reach 43,000 by late March. Following a period of steady decline, daily growth in new cases within the USA should reach less than 1% by the middle or end of April.
Of course these predictions, like any others, should be taken with a grain of salt. Generally, there are three ways to salt them. First, attack the baseline data. Can we trust the statistics from China, South Korea, and Iran, or are there unreported cases in those countries — whether for crowd control or lack of resources — that might distort our comparisons? If so, then predictions of sharp declines in mid to late April are optimistic. Second, attack differences in space and time. Can we compare the experiences of China, South Korea, and Iran, with the experiences of Italy, France, and the United States? Are Chinese populations denser? Was travel restricted in one country earlier than another? What about geography and disjointed clusters? Are there more cigarette smokers in France than South Korea? The same logic applies with differences in time. Can colder January and February weather be compared to warmer March and April weather?
Finally, attack the model. Eyeballing a pattern for a ten- to fifteen-day average following the 1,000 case mark is hardly sophisticated statistics. Even so, China’s average daily growth rate of new cases decayed to less than 1% and a similar pattern can be seen in South Korea. That pattern is now beginning to show in Iran. Of course we need to remain vigilant, but there is good reason to be far more optimistic than popular thinking suggests inasmuch as valid comparisons can be made across countries.
Data is sourced from the World Health Organization COVID-19 Situation Reports, the Johns Hopkins Coronavirus Resource Center, and the Worldometer Coronavirus Database.
 The average daily growth rate of total cases is calculated as the number of people who have tested positive for the virus within the last day divided by the total number of people who have tested positive since the first case was reported.