A Note on Pandemic Mortality Rates

Abstract

This paper considers a population being affected by a mortality stress during a limited period of time. It has recently been suggested that the mortality stress during a pandemic can be viewed as a temporary shift in apparent age. We instead suggest to use a frailty based model where the baseline mortality rate is being stressed. This approach will in a natural way imply post-pandemic mortality rates at the population level.In particular, analytical results concerning the population mortality rate during and after a pandemic are derived. Under general assumptions it is shown that, compared to a non stressed scenario, the mortality is higher during the pandemic and lower after. These general results are exemplified for the Gompertz-Makeham law where more precise results can be obtained using its proportional frailty representation.The results are illustrated based on COVID-19 data for the Swedish population and we estimate the effect of the pandemic on the expected life time of an individual.