Tuesday, July 28On Monday we focused on how to calculate the number of infections from the confirmed cases and the percent of the cases that tested positive. Today, I want to focus on R. And mostly, from then on, we will focus on new emerging data on changes in infections in COVID-19 in the US and elsewhere, and other COVID-19 topics.R is the rate of transmission of an infectious disease. When the disease is ongoing, and the community is responding to it, it is usually referred to as Rt (transmission R) or Re (effective R). There is a special R called R0 (pronounced R-naught and written R-zero). R0 is the measure of how contagious a disease is. If a community does not respond to try to mitigate the disease, and everyone is susceptible, R0 is the rate of growth of the infections.Re or Rt are evaluated as a function of time, while R0 is a constant. Each R is evaluated over the period of reproduction of the virus, which is how long it takes from exposure to the virus for peak infection and transmissibility. For COVID-19, this period is close to 5.2 days. If R is 2, then each 5.2 days the number of new infections would double. The layperson explanation of an R of 2 is that each viral reproductive cycle, each person who is infected will infect two others.The R0 for infamous infectious diseases are well studied, and perhaps none more than measles. Like COVID-19, measles can be transmitted through the air. However, its transmission in the air is much more effective, and its R0 is generally reported as 10. The R0 for influenzas in general range from 1.2 to 1.5. The big swine flu we had in 2009 was reported as a 1.5, and the 1918 pandemic flu had a similar R0. COVID-19 has an R0 that is clearly over 2, and most experts also report it as under 3. This difference between influenza and COVID-19 is why the latter spreads even with strong restriction measures in place.Importantly, in infectious disease, growth or suppression of disease is exponential. Before mitigation measures are taken, COVID-19 grew exponentially, too. As testing was setup in New York City, the number of confirmed COVID-19 cases per day grew 30-fold from 21 to 619 in five days. This same sort of growth happened all throughout the country. You can see this growth is near linear on a semi-log plot, which is typically used to evaluate changes in infections because they feature exponential, rather than linear, growth.So, we have this new measure we want to calculate, Re or Rt. We will leave it to the epidemiologists to calculate R0, because you need to be really careful about using all available data and estimating properly. But a calculation of Rt can be done using deaths, or infections, or hospitalizations. It is simply the ratio change in new infections each 5.2 daysTo calculate R, you take the ratio change in new infections over some length of time, and convert, or prorate, that measure to the ratio over 5.2 days. Why shouldn’t we simply use 5.2 days? All the data on COVID-19 is measured by people, and people work five days of each week. The reporting cycles are slow for two days a week, and prominent changes in cases and deaths are observed in Sunday and Monday reporting.If we calculate R over 5.2 days, it will have weird artifacts from the weekly reporting cycle. To neutralize that cycle, we will measure R over an integral number of weeks, and then prorate it. We find that using two weeks enables R to be calculated so that it tracks reasonably smoothly from day to day. To prorate R from a 14-day ratio to a 5.2 day ratio, we raise it to the (5.2/14) power.Here is a plot of the history of Rt in the state of Georgia going back to early April, calculated over 14 days and prorated to 5.2.In infectious disease, rates of infection go up quickly, but come down slowly. In Georgia, we have had Rt over 2, but never a conversely strong suppression Rt of 0.5 or less. We have to work hard to get Rt down in the 0.8 range – it requires the same suppression that our lockdown in April caused. One month with an Rt of 2 will cause infections to increase 62-fold, which is 2^(31/5.2). How long will it take to cause that much suppression with an R of 0.8? Ninety-six days, which is roughly 0.8^(96/5.2). And that is the reality of infectious diseases that cause pandemics like COVID-19.A community must use staunch restrictions for three times longer than the length of time they let the virus grow. And, if the community relaxes, that exponential growth will simply start right back up, which is what occurred in Georgia immediately after the last phase of re-opening June 13.Now that we have talked about how to calculate infections from cases and test positivity, and how to calculate Rt, on Wednesday we will be able to compare across states and regions in terms of Rt and percent infected. But you should know that rating the risk in a community requires knowing the infection rate and Rt, and that of the two, the infection rate is more important. Its rate of change is more informative about whether the restriction measures in place are adequate or not. Because if people continue to act the same, Rt should stay the same, and new infections should feature exponential growth or suppression.Once again, if anyone wants any of the code I use to make these plots, you can ask at Dave Blake email.