• Stephen Grice

Results for new process for calculating the effective reproduction number from daily positive cases

Updated: May 26

We have developed a new process for estimating the effective reproduction number - Reff - for COVID-19. The process combines an analytic method for calculating Reff from positive test data with a statistical method for generating confidence intervals for the calculation. The process is used to calculate Reff for a selection of countries. The process produces results that compare favourably with other estimation methods such as the EpiEstim method. The math for the new process will be published in a separate technical report on this blog shortly.

While the full results are available in the technical report here. We highlight three examples from the report in this blog post below.

The first country is Italy.

Italy was one of the first European states to have COVID-19 infections after a couple arrived from Wuhan on 23 January. The Italian government response was uneven and the epidemic grew to the point of overwhelming the health system and local authorities ability to respond. Lombardy and other regions were in crisis by early March. On 10 March, Prime Minister Conte announced a "stay at home" order to cover all of Italy, including travel restrictions and a ban on public gatherings. On 21 March, Conte announced further restrictions within the nationwide lockdown, by halting all non-essential production, industries and businesses in Italy, following the rise in the number of new cases and deaths in the previous days. The slow and varied response of the government is reflected in the slow decrease in the effective production number with Reff >= 4.0 on 28 February, decreasing to Reff <= 1.0 on or about 30 March. The Reff <= 1.0 since that time. The EpiForecast nowcast data understates the changes in Reff.

The next country is South Korea.

South Korea introduced what was considered one of the largest and best-organised epidemic control programs in the world. Different measures have been taken to screen the mass population for the virus, and isolate any infected people as well as trace and quarantine contacts of the infected, but did not implement a "stay at home" order. The rapid and extensive tests taken by South Korea have been judged successful in limiting the spread of the outbreak, without using the "stay at home" orders. The rapid and aggressive testing policy lead to a rapid decrease in the effective reproduction number with Reff >= 5.0 on or about 26 February and decreasing to Reff approx. 0.0 by 8 March. Reff <= 1.0 from this date. After a sustained period of reported cases in the country being below 20, a new cluster emerged in central Seoul. A 29-year-old patient from Yongin was found to have visited at least five nightclubs in Itaewon during the late night hours of May 1 and the subsequent early morning hours of May 2. This new cluster resulted in 79 new daily cases being reported by 11 May. This cluster can be seen in the peak in Reff of 2.0 occurring on or about 10 May. The general features of Reff are seen in the EpiForecast nowcast data but are understated and not as detailed. For example the new process shows that the new cluster that occurred on 2 May has been controlled with Reff < 1.0 by about 13 May. This specific feature is not evident in the EpiForecast nowcast data.

The last country is New Zealand.

On 21 March, New Zealand prime minister Jacinda Ardern introduced a country-wide alert level system to deal with the coronavirus outbreak. The alert level was set to 2 immediately. On 23 March, Ardern raised the alert level to 3 and announced the closure of all schools. All sports matches and events as well as non-essential services were required to close in 48 hours. Essential services such as supermarkets, petrol stations, and health services remained open. The social distancing policies had an immediate effect on Reff. Leading into the lockdown Reff >= 4.0. This is possibly due to New Zealanders returning home with the disease. By the second week of April community transmission had stopped and Reff was approx 0.0 on or about 10 April. After this date Reff is undefined as the signal of the epidemic is lost. Of all the countries of the world, the New Zealand data shows the most rapid decline in Reff and New Zealand is one of only a few countries to achieve the World Health Organisation definition of elimination.

The new process shows more accurate and detailed features when hindcasting Reff for all the countries displayed. More information is available in the technical report.


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