Visualizing COVID-19's Effective Reproduction Number (Rt)


The effective reproduction number (Rt) characterizes the COVID-19 spread rate, defined as the average number of secondary infectious cases produced by a primary infectious case. It's used to define the potential for spread at a specific time. If Rt > 1, the virus will spread out and the disease will become an epidemic; if Rt = 1, the virus will spread locally and the disease is endemic; if Rt < 1, the virus will stop spreading and the disease will disappear eventually.

On Dec 16, 2020, we changed the lag for Rt from 5 days to 7 days.

Use slider to adjust date. Click on an area to see its Rt over time.

Click play button to animate Rt over time.

Note the Rt is lagged by 7 days.


Only locations with more than 50 total cases are shown. Occasionally, locations may have negative values for new cases or new deaths because of reporting issues. Full table available for download on Github.

Select areas to compare their Rt.

Note the Rt is lagged by 7 days.

Some areas may not appear in the plot for all time points because of insufficient data.

Occasionally, locations may have negative values for new cases because of reporting issues.

Display a forest plot of Rt for a given resolution

Use slider to adjust date.

Note the Rt is lagged by 7 days.

Some locations might not be shown because of insufficient data.

Select a state to explore.

Note the Rt is lagged by 7 days.


Only locations with more than 50 total cases are shown. Occasionally, locations may have negative values for new cases or new deaths because of reporting issues. Full table available for download on Github.

Website Usage

Rt map tab: This tab shows a map of the Rt by date for various resolutions. Change the date by adjusting the slider. Click the blue “play” button under the slider to animate Rt over time. Change the resolution (Country, US states, US counties, Canadian/Chinese/Australian provinces) using the resolution dropdown menu, and click on a location to see a line graph of the Rt over time and of the number of daily new cases over time. You can scroll to change the zoom of the map and click-drag to move the map around.

Below the map, there is a table of Rts for the chosen date and resolution, as well as the number of new cases, new case rate, cumulative number of cases, number of new deaths, new death rate, and cumulative number of deaths . This table is by default sorted in descending order of Rt, but the sorting can be changed by clicking a column header. Locations where Rt could not be calculated are colored gray in the map and not shown in the table (see Limitations for more info).

Technical note: the blue line is a fitted loess curve to the Rt points, and the error bars show the 95% credible interval of Rt for that time point.

Compare Rt tab: Select states/provinces, US counties, and countries to compare their Rt over time. You can select a location by using the dropdown menu. You can also type the name of the location. Multiple locations for each category (states/provinces, counties, and countries) can be chosen. After you click submit, the results will be displayed as a line plot. Some areas may not appear in the plot because of insufficient data (see Limitations for more info).

Forest Plot tab: This tab shows a forest plot comparing the sorted Rt values of all the countries, all the US states and all the provinces of a few other countries on a given day. The estimated value of Rt is shown as a point, and the error bars give a 95% credible interval. Change the resolution (Country, US states, US counties, Canadian/Chinese/Australian provinces) using the resolution dropdown menu. Locations where Rt could not be calculated are not shown (see Limitations for more info).

Explore States tab: This tab shows an overview for all the counties in a selected US state. The map on the top right shows the Rt for the counties in the state for a selected date. Clicking a county will generate a plot of Rt and number of daily new cases over time on the top left. The plot on the second row on the left left shows the change in Rt over time for counties where Rt was able to be calculated, and the plot on the right shows a forest plot for the counties in the selected state. The date can be adjusted using the slider, and an animation can be shown by clicking the blue “play” button. You can zoom by scrolling and move the map by clicking and dragging. Below the plots, there is a table of Rt for the date selected using the slider. This table is by default sorted in descending order of Rt, but the sorting can be changed by clicking a column header.

Downloading Plots / Maps / Rt

To download a plot, you can right-click on it and select “Save Image As…” Then you'll be able to save the plot to your computer. Right now we do not have a way to save a map, but in the meantime you can take a screenshot. To download the Rt values, case or death counts, and other information shown in the tables, please see the Rt table CSV on our Github page.

If you'd like the shapefiles with Rt information merged that we used for our maps, they are saved as an RDS file on our Github.

Rt Method Description

We calculate and report the daily effective reproduction number (Rt) to characterize COVID-19 spread rate, defined as the expected number of secondary infectious cases produced by a primary infectious case. Rt is used to determine the potential for epidemic spread at a specific time t under the control measures in place (Figure 1, Inglesby, T.V., 2020, reproduced below). If Rt > 1, the virus will spread out and the disease will become an epidemic; if Rt = 1, the virus will spread locally and the disease is endemic; if Rt < 1, the virus will stop spreading and the disease will disappear eventually.