On case-fatality rate: review and hypothesis.

The relationship between log cumulative number of patients (X) and that of deaths (Y) in an epidemic follows the equation logY = klogX - klogN(0), where k is a constant determining the slope and N(0) is the value of X when Y = 1. Diseases with k = 1 are Ebola hemorrhagic fever, avian influenza H5N1, cholera, and hand, foot, and mouth disease; those with k > 1 are the influenza H1N1 2009 pandemic in countries other than Mexico and the SARS epidemic in some countries; and those with k < 1 include the influenza H1N1 2009 pandemic in Mexico. Epidemics with k > 1 can be simulated by postulating two subpopulations (normal population [NP] and vulnerable population [VP]), where the epidemic proceeds at higher speed and at higher mortality in VP than in NP. Epidemics with k < 1 can be simulated by postulating coexisting high virulence virus (HVV) and low virulence virus (LVV), with the former being propagated at slower speed and with a higher mortality rate than the latter. An epidemic with k > 1 was simulated using parameters that are fractions of subpopulations NP or VP from the total population (f) and NP- or VP-specific patient multiplication (M) and mortality (D) rates. An epidemic with k < 1 was simulated using parameters that are fractions of HVV- or LVV-infected human populations (f), and HVV- or LVV-specific M and D.