The COVID-19 pandemic has been a sobering reminder of the extensive damage brought about by epidemics, phenomena that play a vivid role in our collective memory, and that have long been identified as significant sources of risk for humanity. The use of increasingly sophisticated mathematical and computational models for the spreading and the implications of epidemics should, in principle, provide policy- and decision-makers with a greater situational awareness regarding their potential risk. Yet most of those models ignore the tail risk of contagious diseases, use point forecasts, and the reliability of their parameters is rarely questioned and incorporated in the projections. We argue that a natural and empirically correct framework for assessing (and managing) the real risk of pandemics is provided by extreme value theory (EVT), an approach that has historically been developed to treat phenomena in which extremes (maxima or minima) and not averages play the role of the protagonist, being the fundamental source of risk. By analysing data for pandemic outbreaks spanning over the past 2500 years, we show that the related distribution of fatalities is strongly fat-tailed, suggesting a tail risk that is unfortunately largely ignored in common epidemiological models. We use a dual distribution method, combined with EVT, to extract information from the data that is not immediately available to inspection. To check the robustness of our conclusions, we stress our data to account for the imprecision in historical reporting. We argue that our findings have significant implications, including on the extent to which compartmental epidemiological models and similar approaches can be relied upon for making policy decisions.

COVID-19大流行使人警醒地意识到了流行病所造成的广泛破坏，这些现象在我们的集体记忆中起着生动的作用，长期以来一直被认为是人类重大风险的来源。原则上，使用日益复杂的数学和计算模型来传播流行病及其影响，原则上应为政策制定者和决策者提供有关其潜在风险的更大的态势感知。然而，大多数模型都忽略了传染性疾病的尾巴风险，使用点预测，并且很少质疑其参数的可靠性并将其纳入预测中。我们认为，极值理论（EVT）为评估（和管理）大流行的实际风险提供了一种自然的，基于经验的正确框架，历史上已经开发出一种方法来处理极端现象（最大值或最小值）而不是平均值充当主角的角色，而主角是风险的基本来源。通过分析过去2500年中大流行暴发的数据，我们表明死亡人数的相关分布是严重的尾巴分布，这提示不幸的是，在常见的流行病学模型中，尾部风险被很大程度上忽略了。我们使用结合EVT的双重分发方法从无法立即检查的数据中提取信息。为了检查结论的可靠性，我们强调数据要考虑历史报告中的不精确性。我们认为我们的发现具有重大意义，