The effective reproductive number ($R_t$) is one of the major outcomes we report on covidestim.org. $R_t$ represents the average number of new infections produced by a single infectious individual at time $t$, taking account of current mitigation measures and transmission patterns, as well as features of the virus that make it more or less likely to be transmitted. If $R_t > 1.0$, each infection produces more than one future infection and the epidemic will grow. If $R_t<1.0$, each infection produces less than one future infection and the epidemic will decline. For this reason, $R_t$ is a key measure for understanding SARS-CoV-2 transmission patterns.
In covidestim, we fit an epidemiological model to the time-series of reported COVID-19 diagnoses and deaths, then back-calculate $R_t$ using two quantities: the day-to-day change in total SARS-CoV-2 infections ($A_t$, representing total infections on day $t$), and an estimate of the serial interval (used a proxy for the generation interval $z$, the average number of days delay between an initial COVID-19 infection and the next generation of infections they produce). With these quantities, $R_t$ can be calculated directly (more details to be found here):
$$R_t = \bigg(\frac{A_{t+1}}{A_t}\bigg)^z$$
So, if infections increase by 10% between one day and the next, and assuming a serial interval of 5.8 days (the mean value we use in the model), that produces an $R_t$ of $1.1^{5.8} = 1.74$. As the serial interval is assumed to be constant over time, $R_t$ is a measure of the daily percentage change in SARS-CoV-2 infections. While this relationship is (relatively) straightforward, the reported $R_t$ values can be misleading if interpreted in isolation.
Firstly, it is important to know that the “real-time” estimate of $R_t$ (e.g. an estimate of $R_t$ for today, based on data reported today) is very uncertain. This is because the data we have to estimate $R_t$ (daily diagnoses and deaths, as reported by each county and state) are lagged relative to transmission. Today’s reported diagnoses have resulted from transmissions that happened 1-2 weeks ago on average, and today’s reported COVID-19 deaths relate to transmission that happened even further in the past. While we assume that $R_t$ is unlikely to change abruptly, we have very little evidence on what $R_t$ is today. This will be true of all estimation approaches that make use of conventional surveillance data. This uncertainty can be seen in the wide credible intervals for $R_t$ shown in our state-level results (in the figure below, the left panel shows the most recent $R_t$ estimates for Arizona on September 26th). By a traditional interpretation of our 95% intervals, we believe there is a 1-in-20 chance that the true value of $R_t$ is outside the interval on any given day. While we don’t show intervals for the county-level results, the uncertainty in $R_t$ is revealed by the sometimes major revisions in $R_t$ that can be seen in the country-level results (figure below, right panel). Even if the most recent point estimate for $R_t$ is above 1.0, it could be revised to a value below 1.0 when more data come in, and vice-versa.
Secondly, the implications of $R_t$ should be understood in light of current levels of transmission. Even if $R_t$ has a value of 0.91, consistent with a declining epidemic, this could imply a long period of elevated transmission – and associated illness, hospitalization and mortality – if starting from a point of high transmission. For example, with an $R_t$ of 0.91 it would take more than 6 weeks to see a 50% drop in transmission. In these situations, it is important to achieve more rapid reduction in transmission, both to minimize health losses and to reduce the risk of further resurgence in infections. So, while lower values of $R_t$ imply less transmission than higher values (all else being equal), and $R_t<1$ implies that the number of new infections has started to decrease, it is important to interpret these estimates in light of their uncertainty and the limits on what they tell us about both the short-term and longer-term trajectory of the epidemic.