Exponential distribution of large excess death rates in Europe during the COVID-19 outbreak in the spring of 2020

Excess death rates E during the spring of 2020 are computed in N = 540 level 3 European territorial units for statistics —NUTS3 in Belgium (40), France (96), Italy (110), Netherlands (44), Spain (50), Sweden(21) and United Kingdom (179)— from 2020 provisional week deaths, the population numbers for 2020, and observations in previous years (reference or baseline), all of them obtained from Eurostat web page.

Excess death rates are classified in three tiers. Largest 27 excess death rates (tier 1, E > 1721 × 10 ⁻⁶ ) were distributed exponentially with empirical complementary cumulative distribution function (empirical survival function) S following S ∝ 2 ^{− E/ε} with ε ₁ = 958(42) × 10 ⁻⁶ . Tier 2 (the next 52 largest excess death rates, E < 1142 × 10 ⁻⁶ also distributed exponentially with ε ₂ = 379.5(89) × 10 ⁻⁶ . Tier 3 (smallest 460 excess death rates) were distributed normally.

The results suggests that when, within some regions, the outbreak is above a threshold, interaction with neighbouring region become less relevant and the outcomes —excess death rates— become exponentially distributed as it happens with independent events.