# How is the duration of an epidemic defined?

I've come across papers that plot the duration of an epidemic using a parameterized model, and papers that calculate the expectation of the duration. But I'm looking for how the duration is defined.

At least one paper gave indications that it was taken to be the time at which the number of infected individuals peak. I guess is OK if you consider that epidemic isn't normally used to refer to the situation where number of infected people decline starting from time zero, i.e., there is no period of growth. I also guess that one way for this to happen is if some experimental virus gets released, infecting a lot of people locally, but it is not easily transmitted.

Even if there was a period of growth followed by decline, however, I naturally think of duration as the width of the pulse. For example, optical pulse widths are often measured using full width at half maximum. So I'm wondering if there is a commonly accepted formal definition that recognizes the end time of the epidemic, e.g., perhaps based on how near it gets to steady-state conditions (notionally at time infinity) or some other intuition-motivated criterion.

• I suspect there's more than one definition. In simple models (total immunity gained post-illness) it's simply the time to the number of infected or susceptible to drop to zero.
– Fizz
Apr 17 '20 at 12:32
• Thanks, Fizz. Did you want to post that as the answer? Susceptibles don't necessarily drop to zero, so the more general answer is when infected drop to zero. Apr 17 '20 at 12:49

In https://www.who.int/emergencies/diseases/managing-epidemics-interactive.pdf the WHO defines stages for epidemics. In this file there is also this description of the last stage:

Elimination or eradication: Control of a disease may lead to its elimination, which means that is sufficiently controlled to prevent an epidemic from occurring in a defined geographical area. Elimination means that the disease is no longer considered as a major public health issue. However, intervention measures (surveillance and control) should continue to prevent its re-emergence. Eradication of a disease – much more difficult and rarely achieved - involves the permanent elimination of its incidence worldwide. There is no longer a need for interventions measures. Three criteria need to be met in order to eradicate a disease: there must be an available intervention to interrupt its transmission; there must be available efficient diagnostic tools to detect cases that could lead to transmission; and humans must be the only reservoir.

For pandemics there are also stages, described here: https://www.ncbi.nlm.nih.gov/books/NBK143061/

For the 2009 influenza pandemic there is a nice graphic outlining its stages:

Also, during the Ebola outbreak the end of the outbreak was defined as no new Ebola case within two incubation periods (https://www.who.int/csr/disease/ebola/declaration-ebola-end/en/).

• Thanks, Thomas. It looks like the "end" of an epidemic is vaguely defined, since even the word "epidemic" is vaguely defined. Apr 20 '20 at 20:37