How Are We Doing?

One month into reopening in Tennessee, how are things going? One of the predictions made is that the transmission of the virus would increase once restrictions on businesses were lifted and people started moving around more. There has been an increase in the number of new cases each day in both Tennessee and Alabama, but so far neither state is back on an exponential growth curve. At the end of April, Tennessee was averaging 250 new cases a day and Alabama was averaging 150. Over the last week, that has increased to roughly 400 new cases a day in both states. See the graph below for a comparison.

What this graph shows is that the reproduction rate of the virus has increased as both states have re-opened. Estimates from two websites, https://rt.live/ and https://covid19-projections.com, show that for both states that this has increased over the last month. The reproduction rate is the number of people, on average, to which an infected person spreads the disease. If the reproduction rate is greater than 1, the spread is growing, and if it is less than 1, the spread is shrinking. The average of the two estimates for these estimates four weeks ago for Tennessee was 0.95 and for Alabama it was 0.99. The current average estimate for Tennessee is 1.05 and for Alabama it is 1.06. If these are accurate, the growth was contained a month ago, but is now beginning to spread again. These numbers are still below the reproduction rates before the shutdown, which were approximately 1.8 for Tennessee and 2.0 for Alabama. We are not back to exponential growth (yet). As some people are being cautious and wearing masks and still continuing to practice social distancing, I don’t think we will return to those levels in the near future. The two questions outstanding are:

• How high does the reproduction rate have to go to get back to exponential growth? If it does, this will likely trigger another shutdown.
• How high will the reproduction rate grow? It is currently increasing and plans are to continue relaxing restrictions, so it will likely continue to increase. Some studies indicate a seasonal influence, but the true impact of that is so far unknown. Also, schools are out for summer, which is one possible avenue for the rapid spread.

To answer these questions for Tennessee, we turn to the SIR model that is designed to estimate the spread of infectious diseases like COVID-19. This model has its shortcomings, but some of the most accurate models, like the COVID projections model we mentioned earlier, use only a slightly more sophisticated version of this model (called SEIR).

Using the SIR mode, see the graph below for a comparison of the impact of the reproduction rate R on the cumulative number of reported cases.

If the reproduction rate were to increase back to 1.4 in the near term, we would be back to exponential growth and there would likely be another shutdown in the near future. Given that some people are taking precautions, I think this is likely the worst case in the near-term. Combined with some seasonal impact on COVID and the fact that schools are out, I think the most likely scenario is that the reproduction rate will slowly increase to 1.25 by July and remain at that level until the end of August. This will mean an additional 1,400 deaths during June-August, in addition to the 356 already recorded. This is not a calamitous outcome in the near-term, but it means we are slowly unflattening the curve. There likely will not be a second shutdown in the next three months, but we are setting ourselves up for a potential return to exponential growth this Fall.