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The Math of Epidemics

Lingo in the media are sometimes confusing or downright erroneous. This post tries to make the definitions clearer.

Case Fatality Rate (CFR) = (number of deaths) / (number of confirmed cases of the disease that have resolved)

The number of confirmed cases of the disease that have “resolved” means that we’re only counting those cases that have resulted in either recovery or death. Now there may still be people who are infected but have not yet recovered or not yet died. We’re not considering those in the denominator. Resolved cases means either the persons recovered or the persons died.

The difficulty with CFR is that the number of confirmed cases may not be accurately reflected. With a novel disease, it is difficult (especially in the beginning stages) to actually confirm a case due to the lack of testing and the lack of information regarding the characteristics of a pathogen. However, the CFR can help us understand the pathogen better, because scientists can look at data in a different way. Examples are (but not limited to): population by age groups; geographical locations; and other comorbidities.

Two other numbers (Infection Fatality Rate and Crude Mortality Rate) gives information about the risk of dying.

Infection Fatality Rate (IFR) describes the risk of dying if someone is infected. A population X is studied and the number of infections (V) within that population is counted. Out of those counted infections (V) of population X, F is the number of fatalities. Thus, the IFR for population X may be expressed as:

IFR = F / V

Crude Mortality Rate (CMR) is a number that describes the risk of dying relative to the entire population.

Crude Mortality Rate = (number of deaths) / (number of at-risk population)

Please take a few minutes to watch this video (below) by The Guardian. I, myself, was getting confused by all these “rates” until I slowed everything down and digested the video. I’ve read many articles and posts, and the video below is the best explanation with helpful animations.

https://youtu.be/sMtzWVTPmLI

References