This post starts a daily analysis of the spread of the Covid19 virus in different countries.
When considering the delay of the onset of the contagion in different locations and the different scales in terms of number of deaths and active cases, it is often difficult to draw these comparisons.
The aim of this series is to spot patterns indicating the effect of different government policies in tackling the spread of the virus. First of all we need a good indicator with daily frequency. Since the number of active cases depends strongly on the testing policy adopted, the number of positives is not an indicator without bias, in my opinion. Moreover, the testing policy of a given country will change during the development of the infection. Typically more accurate tests at the beginning of the curve are followed by testing only hospitalized cases, when the health service is overwhelmed. This produces an unrealistic morbidity rate, like the 10% rate for Italy, wrongly attributed to a mutation of the virus.
The only objective indicator in my opinion, even when under-estimated, is the total number of deaths. This is published daily for different countries and can be easily recorded in a time series.
Clearly a death today is caused by an infection about three weeks in advance, hence this indicator will have an intrinsic time lag of about this time. Only when considering this lag it is possible to correlate the public health measures taken with this response.
With this in mind we want to see how the decisions taken affect the curve dynamics, mostly its shape and slope. Two derived indicators of interest are therefore:
- The doubling time, i.e. the number of consecutive days required for a doubling of the total number of deaths. Good public health measures should see this number increase with time;
- The growth-rate of the daily number of fatalities; good measure should see this number stabilizing first to zero, before starting to decrease.
Technically we define:
- C(d) the cumulative number of fatalities at day d
- N(d)= C(d)-C(d-1), the daily increment of fatalities
- R(d) = N(d)/N(d-1) – 1, the daily growth rate
- R3(d) = (N(d)/N(d-3))^(1/3) – 1, as the geometric average of R(d) at time d. This the growth-rate defined above
- D(d) = LN(2)/LN(1_R3(d)) the doubling time, where LN is the natural logarithm.
The analysis is followed by plotting the daily curves of R3 and D for different countries.