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We analyse the dynamic evolution of disease outbreak risk after the main waves of the 1918-19 “Spanish flu” pandemic in the US and in major cities in the UK, and after the 1890-91 “Russian flu” pandemic in England and Wales. We compile municipal public health records and use national data to model the stochastic process of mortality rates after the main pandemic waves as a sequence of bounded Pareto distributions with an exponentially decaying tail parameter. In all cases, we find elevated mortality risk lasting nearly two decades. An application to COVID-19 under model uncertainty shows that in 80% of model-predicted time series, the annual probability of outbreaks exceeding 500 deaths per million is above 20% for a decade, remaining above 10% for two decades.

We analyse the dynamic evolution of disease outbreak risk after the main waves of the 1918-19 “Spanish flu” pandemic in the US and in major cities in the UK, and after the 1890-91 “Russian flu” pandemic in England and Wales. We compile municipal public health records and use national data to model the stochastic process of mortality rates after the main pandemic waves as a sequence of bounded Pareto distributions with an exponentially decaying tail parameter. In all cases, we find elevated mortality risk lasting nearly two decades. An application to COVID-19 under model uncertainty shows that in 90% of model-predicted time series, the annual probability of outbreaks exceeding 500 deaths per million is above 20% for a decade, remaining above 10% for two decades.