The Rt is the most important characteristic of an outbreak, indicating how many persons are eventually infected on average by a newly infected individual. When the Rt is greater than 1, then the outbreak is spreading exponentially, while less than 1 indicates that the outbreak is decaying and will eventually go extinct.
The most precise way to calculate the Rt is directly from medical records that indicate who infected whom. However, this is not really feasible in the current Covid-19 pandemic, because such data are not available for most countries. In the absence of knowledge about infection transmission chains, advanced statistical methods can help to fill this gap. Previous research during the last 20 years have shown that so-called Bayesian inference can be used to estimate most likely infection transmission pathways, which, in turn, allows calculation of the Rt. Our team has relied on these established algorithms and further improved them to calculate the Rt curves for each country. As an input, we primarily use the new infection incidence data that are reported daily. We update our Rt estimations twice a day..
Policy makers need to have access to a reliable measure of whether their country’s epidemic is accelerating or is under control in order to make rational decisions about intensifying or relaxing lockdowns and various under costly interventions. For example, because lockdowns cause an immense economic harm, they could be relaxed if the risk of the epidemic spreading is low. However, because of the inherent randomness of how an epidemic is evolving, it is difficult to gauge how intensely the epidemic is spreading by simply considering the daily reports on newly infected individuals. In particular, such curves often show zigs and zags, and incostincecises between different days. The Rt estimation algorithm, used in this site, integrates long time delays between a transmission of infection and also testing, producing smooth curves in near real time. If the Rt is significantly higher than 1, for example, higher than 2, then the policy makers should strongly consider tightening measures. On the other hand, if the Rt is near 1, or preferably significantly below 1, then this could suggest that relaxing measures could be potentially considered.
Several governments, including the USA and the UK, have relied on teams of mathematical modelers to inform policy decisions. Often, in such so-called SIR models, the Rt enters as a key input parameter. More sophisticated models vary the Rt by considering how measures such as quarantines reduce people’s contacts with each other, hence reducing the Rt. However, the worldwide survey of the Rt presented in this web site is rather unique, and could provide important new insights to the public, the policy makers and also to mathematical modelers.
They are related, but in a very convoluted way. The slope by itself is not very meaningful for several reasons: 1) Most data is very noisy, so the slope is not well defined (i.e. the zig-zagging problem mentioned above) 2) Even if the real Rt is going down, the slope can temporarily go up because a week earlier there was a spike of infections, hence, overall leading to wrong conclusions 3) Because of 1) and 2), it may not be meaningful to quantitatively compare countries with each other. In the absence of an Rt estimate, the slope can be used as a rough substitute, however, its quality as a gauge epidemics’ spreading is rather poor.
If only a fraction of sick individuals is tested, then our Rt estimate should still be accurate as long as the testing coverage stays constant in time. However, if testing coverage increases over time, that would lead to overestimation of more recent Rt values. There are some ways to account for such an increase in modeling, which we plan to do in a future update.
For our current model what is important to remain constant is not the testing volume, but the fraction of unreported cases (even if it is very high, say 80%). However, if due to additional new testing and other government measures the underreporting fraction goes down over time (which is naturally expected to some degree), that would tend to inflate the Rt values. Based on some reasonable assumptions about underreporting diminishing over time, it should be possible in the future to account for this effect.
Usual ways to estimate the Rt would lead to about 3-weeks time lag, which is not satisfactory in a fast moving epidemic. There are some ways to reduce this time lag to about 5 days, which we have implemented. This, however, introduces a systematic underestimation error. For Rt values up to 1.5, the error is very small, less than 0.05. The error grows for larger Rt values: for example, there is 0.1-0.3 underestimation when the Rt is near 2.0. .We are currently working on developing a novel algorithm to reduce these underestimation errors for high Rt values.
For each country, we run 1,000 simulations, which allows us to quantify the random error in our Rt estimate. For each timeslice, we calculate not only the average of the Rt but also its variance. The light-blue-shaded areas show a region of one standard deviation from the average.