  Different ways of calculating mortality ratios during epidemics have yielded
very different results, particularly during the current COVID-19 pandemic. We
formulate both a survival probability model and an associated infection
duration-dependent SIR model to define individual- and population-based
estimates of dynamic mortality ratios. The key parameters that affect the
dynamics of the different mortality estimates are the incubation period and the
time individuals were infected before confirmation of infection. We stress that
none of these ratios are accurately represented by the often misinterpreted
case fatality ratio (CFR), the number of deaths to date divided by the total
number of confirmed infected cases to date. Using data on the recent SARS-CoV-2
outbreaks, we estimate and compare the different dynamic mortality ratios and
highlight their differences. Informed by our modeling, we propose more
systematic methods to determine mortality ratios during epidemic outbreaks and
discuss sensitivity to confounding effects and uncertainties in the data.
