Quantifying the impact of the response
Quantifying changes in the rate of spread of infection over the course of an epidemic is critical for monitoring the collective impact of public health interventions and forecasting the short-term clinical burden. A key indicator of transmission in context is the effective reproduction number (R𝑒𝑓𝑓) — the average number of secondary infections caused by an infected individual in the presence of public health interventions and for which no assumption of 100% susceptibility is made. If control efforts are able to bring R𝑒𝑓𝑓 below 1, then on average there will be a decline in the number of new cases reported. The decline will become apparent after a delay of approximately one incubation period plus time to case detection and reporting following implementation of the control measure (i.e., at least two weeks).
Using case counts from the Australian national COVID-19 database, we estimated R𝑒𝑓𝑓 over time for each Australian state from 24 February to 5 April 2020 (Figure 2). We used a statistical method that estimates time-varying R𝑒𝑓𝑓 by using an optimally selected moving average window (according to the continuous ranked probability score) to smooth the curve and reduce the impact of localised clusters and outbreaks that may cause large fluctuations (London School of Hygiene & Tropical Medicine Mathematical Modelling of Infectious Diseases nCoV working group, 2020). Importantly, the method accounts for time delays between illness onset and case notification. Incorporation of this lag is critical for accurate interpretation of the most recent data in the analysis, to be sure that an observed drop in the number of reported cases reflects an actual drop in case numbers.
Results show that R𝑒𝑓𝑓 has likely been below one in each Australian state since early-to-mid March. These estimates are geographically averaged results over large areas and it is possible that R𝑒𝑓𝑓 was much higher than one in a number of localised settings (see Figure 2). The estimated time-varying R𝑒𝑓𝑓 value is based on cases that have been identified as a result of local transmission, whereas imported cases only contribute to the force of infection. Imported and locally acquired cases were assumed to be equally infectious. The method for estimating R𝑒𝑓𝑓 is sensitive to this assumption. Hence, we performed a sensitivity analysis to assess the impact of stepwise reductions in the infectiousness of imported cases on R𝑒𝑓𝑓 as a result of quarantine measures implemented over time (see Figure 2—figure supplement 1, Figure 2—figure supplement 2, and Figure 2—figure supplement 3). The sensitivity analyses suggest that R𝑒𝑓𝑓 may well have dropped below one later than shown in Figure 2.
In Victoria and New South Wales, the two Australian states with a substantial number of local cases, the effective reproduction number likely dropped from marginally above one to well below one within a two week period (considering both our main result and those from the sensitivity analyses) coinciding with the implementation of social distancing measures. A comparable trend was observed in New Zealand and many Western European countries, including France, Spain and Germany (London School of Hygiene & Tropical Medicine Mathematical Modelling of Infectious Diseases nCoV working group, 2020), where similar national, stage-wise social distancing policies were enacted (Flaxman et al., 2020). However, most of these European countries experienced widespread community transmission prior to the implementation of social distancing measures, with R𝑒𝑓𝑓 estimates reaching between 1.5 and 2 in early March and declining over a longer period (three to four weeks) relative to Australia.