Using Emperical Death Data to Qualify Progression of Covid 19

What follows are several sovereign geography charts of the z-score (standardized) rolling 10 day slope of cumulative deaths.

Sweden is the base case given the integrity of the Sweden death data and the weekly summary of the covid 19 results for the week, the near future policy applied and forthright criticism of policy failings or successes.

Sweden’s strategy is now well known and, briefly put, the strategy pragmatically faced the realities of covid 19, did not have state applied lock down, and looked to citizens to become educated and then apply their own response to covid 19.

This resulted - for good or for bad - with what might be considered a “natural” progression of covid 19 when the state did not impose a lock down and looked to common sense.

The standardized or z-score 10 day rolling slope of the cumulative deaths is derived.  The z-score is used so as to compare countries of different size, heterogeneity or homogeneity, and with different strategies of suppression or mitigation.  

The z-score of slope provides common measurement of the rate of change of the epidemic. USing deaths sidesteps the problems of greatly differing testing policy and thereby greatly differing level and cumulative number of infections.  Throughout the world cases resulting from testing produce a “case fatality rates” (“CFR”) of 3% to 8% while the consensus of infection fatality rates is, depending on age and other characteristics of the infected, is 0.2% to 0.7%.  This means cases are not useful in understanding the current status of the disease or its progression to date.

The z-core is plotted against time and also against the derived % of the geography population using a 0.5% infections fatality rate (“IFR”). While geographys will have various IFR rates, the range being likely 0.2% to 0.7%, the consistent 0.5% IFR is useful to provide a consistent comparison across countries.

Sweden

Sweden is useful as a base case given the transparency of the policy and data that is clean. While Sweden did have excess mortlaity associated with covid 19, this was only for the first few weeks in March. Thereafter Sweden tested all deaths and if a death tested positive it was certified as a covid 19 death. This is not to have a view as to whether or not Swedish policy was good or bad, just to illustrate what the epidemic’s results will be given only personal suppression and lockdown, no masks insisted upon, and seeking “buy-in” from a chosive populace that has demonstrated a tradition of unity and shared common sense.

Note the z-score mapped to % of the population infected rose towards 4 over time and then dropped towards a 0 value with the population infected (using 0.5% IFR) just below 15%. It can be considered that the heterogeneity of Sweden and their demonstarted social common sense using transparency and close interaction with those with “competency” (Anders Tegnell et al) has reached an effective herd immunity. The formula for herd immunity threshold (’HIT") is well known:\[1-(1/R)\]

Popular belief, which seemed to be embedded since Imperial College Ferguson grim forecasts made in February, is that it is the intial R which is used to define R, leading to a 60% to 80% HIT. However as Sweden shows it is the latest sustainable R which defines HIT. That is a HIT of 14% to 15%.

A rethink of what is herd immunity threshold is underway. “Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics” by Gomes et al in a medRxiv pre-print, providing a conceptual to see Sweden at HIT at 15%. From the pre-print: “Herd immunity thresholds are then calculated as \(1-(1/R0)1/(1+CV2)\) or \(1-(1/R0)1/(1+2CV2)\), depending on whether variation is on susceptibility or exposure.”

The area under the z-score to % of the populace infected for Sweden is calculated:

19.2 = \(\int ZScore\)

A table of the various contrie integral value for the z-score will be provided. Sweden indicates the integral should approach at least 20 as long as the z-score value is well under .5 . Those countries which are not near HIT will have a z-score well above .5 and have integral values as great as 40 or more (Brazil below), indicating that HIT is yet to be approached.

A low integral under 15 indicates that there is likelihood of another wave of the epidemic to come.

All geographies will in the end reach HIT, with integral values 15 or higher and the z-score value under .5 and approaching 0. This also coincides with a % of the populace infected of at least 12%. Those countries with % if infected or only pausing and will, without a vaccine, all eventually reach 12% of the populace or greater infected. Those countries which have not sustained a R lower than 1.7 to 1.8 will have HIT of 30% or higher.

Therefore it is likly that those countries which are claiming success in the epidemic - Singapore, South Korea, Japan and others are to experience additonal waves of the epidemic until at least 14% of the populace is infected. Those countries that are starting to see a rise in z-score after reaching low under .5 values yet with well under 5% to 8% of the populace infected will have a rough go going forward.

The SWE z-score to % of the populace infected: 19.2 = \(\int ZScore\)

The USA z-score to % of the populace infected: 43.8 = \(\int ZScore\)

The GBR z-score to % of the populace infected: 19.9 = \(\int ZScore\)

The CAN z-score to % of the populace infected: 8.7 = \(\int ZScore\)

The FRA z-score to % of the populace infected: 14.9 = \(\int ZScore\)

The NOR z-score to % of the populace infected: 1.4 = \(\int ZScore\)

The ITA z-score to % of the populace infected: 18.4 = \(\int ZScore\)

The ESP z-score to % of the populace infected: 21.7 = \(\int ZScore\)

The IRL z-score to % of the populace infected: 10 = \(\int ZScore\)

The BRA z-score to % of the populace infected: 47.4 = \(\int ZScore\)

The SGP z-score to % of the populace infected: 0.1 = \(\int ZScore\)