Canaries in the Mine: An Update

by Rudolph Kalveks

This was the snapshot of the parameters that describe the shape of the Coronavirus epidemic in terms of simple SIR models, based on the death statistics up to June 7th, shown in Table 1 of Canaries in the Mine:

We can repeat the analysis making use of the additional death statistics over the two weeks up to June 21st.

We observe that over this two week interval:

1. There has been no substantial change in any of the parameters in Europe, USA, Australia.
2. In particular, the parameter gamma for fatally susceptible sub-populations has only fluctuated by a couple of percent in these countries over the two weeks.
3. Parameters for fatally susceptible sub-populations are looking better in South Africa, but worse in Brazil and India, and also worse globally.

In conclusion, although the epidemics are obviously further progressed, over the last two weeks there has been no signal for any material change in the shape of the epidemic SIR model curves in Europe, the USA and Australia. Thus, the relaxation of lockdowns (well documented elsewhere) has so far had no discernible impact on the recovery from the epidemic in these countries.

This undermines the analysis by Flaxman et al (published June 8th in Nature) that continues to predict a tenfold increase in the population at risk from the relaxation of lockdown restrictions.

Globally, however, several regions are still at an earlier stage in the epidemic, and the parameters of the estimating model are responding to new information about the progress of the epidemic (and to data noise). The long half-life parameters for Brazil and India can be expected to reduce in due course towards values more typical of those countries with advanced epidemics.

Figure 1. The orange data points are cumulative deaths, as reported daily by Worldometer, starting from the first recorded death until June 21st, 2020. The solid curves represent the minimal SIR model. Calculations carried out using Mathematica.

Figure 2. The three SIR model sub-populations are Susceptible (blue), Infected (orange) and Resolved (green). The vertical scale counts cumulative deaths. The horizontal scale counts days from the first recorded death, with the vertical red line indicating the most recent data (June 21st, 2020). Calculations carried out using Mathematica.

Figure 3. Epidemiological R. The horizontal scale counts days from the first recorded death, with the vertical red line indicating the most recent data (June 21st, 2020). Calculations carried out using Mathematica.

Dr Rudolph Kalveks is a retired executive. His PhD was in theoretical physics.