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Extreme value theory and the probability of extreme novel epidemics

This Club EvMed event occurred on February 15, 2024. Learn more about Club EvMed at

This conversation was led by Dr. Marco Marani & Dr. William Pan.

Human-natural processes that generate extreme events with large financial, social, and health consequences, are inherently non-stationary due to ever-changing anthropogenic pressures and societal exposure. The issues posed by non-stationarity are recognized in Earth system science and are being addressed with a variety of tools and varying degrees of success. These developments are possible because a large amount of observational and modelling information is available. Extensive epidemiological information remains fragmented and virtually unexplored from this perspective due to the lack of approaches to leverage observations of a heterogeneous past. To address this gap, here we describe and analyze a long historical record (1600-present) of infectious disease epidemics assembled from existing literature. This new record enabled the development and applications of methods to quantify the time-varying probability of occurrence of extreme epidemic events. We define the intensity of epidemic events, the number of deaths/time/global population, and find that observations from several hundred years, covering almost four orders of magnitude of epidemic intensity, follow a probability distribution with a slowly-decaying power-law tail (Generalized Pareto Distribution, asymptotic exponent = -0.71). To the contrary, the yearly number of epidemics is non-stationary, implying that conventional extreme value analyses are inappropriate. We find that the rate of occurrence of extreme epidemics varies nine-fold over centennial time scales, from about 0.4 to 3.6 epidemics/year. As a result, yearly occurrence probabilities of extreme epidemics are far from constant: The intensity computed for the most extreme event on record – the “Spanish Influenza” of 1918-1920 – has a probability of occurrence varying from 0.11 to 0.89 %/year in the time frame from 1600 to present. A COVID19-like event is estimated currently having a probability of occurrence of 0.19 % / year. Should the probability of emergence of new diseases remain constant, this translates to a probability of 17% of observing such an event in one’s lifetime.

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