One of my readers thinks the public needs an education on the nature of exponential growth (and decline) in regard to SARS-Cov2 infection. I think he’s right.
So, I’ve constructed two graphs using the concepts of R0 and Re. R0 is an inherent property of bacteria and viruses and represents the number of individuals that are typically infected by one individual. You will recall that R0 is an average but has a fat tail due to superspreaders. Re represents the effective R0 when social, ecological, and other factors are taken into account. In the case of the pandemic those factors include things like social distancing, mask wearing, and the density of a population. In the case of our current pandemic, Re is usually less than R0 for most geographic regions but can be much higher in hotspots.
An R0 of one means that one person typically infects only one other person. Values less than 1 mean that most of the contacts between the infected person and other contacts don’t result in the contacts becoming infected; for example, an R0 of 0.7 means that 10 people typically infect 17 people. On the other hand, an R0 greater than 1 means that more than one person is infected by someone with the disease.
Change in infection rate for R0 of 0.6, 0.9, and 1.1
In Figure 1 the units on the X axis of the graph represent successive incubation periods, meaning the time between when a person is infected and is capable of infecting others. For SARS-Cov2 this is about 6 days on average. So, the time between each unit on the axis is about 6 days. Notice the big difference over time between an R0 of 0.9 and 1.1. After about 20 cycles (about 3 months) we have added nearly 600,000 infected cases with an R0 of 1.1 while they have declined to about 10,000 over the last cycle. Note that these are just additional cases not the cumulative totals. These are all examples of exponential curves.
Change in infection rates between an R0 of 1.8 and 2.4, representing the effect of a new aggressive strain such as B.1.1.7
In Figure 2 we can see the difference between an R0 of 1.8 and 2.4. This difference represents the effect of a multigroup set of mutations, typical of the B.1.1.7 strain (estimated range 0.4 to 0.7). Now you should have a better appreciation of the nature of exponential growth and decline of viral epidemics/pandemics and why I am so concerned about the new SARS-Cov2 strains that have emerged. You can also see that once you get below an R0 of 1 the infection rate can decline dramatically, which is just as important to understand, because that’s the goal with vaccination!