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.
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In 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: 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/).
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