  Nonpharmaceutical interventions (NPI) such as banning public events or
instituting lockdowns have been widely applied around the world to control the
current COVID-19 pandemic. Typically, this type of intervention is imposed when
an epidemiological indicator in a given population exceeds a certain threshold.
Then, the nonpharmaceutical intervention is lifted when the levels of the
indicator used have decreased sufficiently. What is the best indicator to use?
In this paper, we propose a mathematical framework to try to answer this
question. More specifically, the proposed framework permits to assess and
compare different event-triggered controls based on epidemiological indicators.
Our methodology consists of considering some outcomes that are consequences of
the nonpharmaceutical interventions that a decision maker aims to make as low
as possible. The peak demand for intensive care units (ICU) and the total
number of days in lockdown are examples of such outcomes. If an epidemiological
indicator is used to trigger the interventions, there is naturally a trade-off
between the outcomes that can be seen as a curve parameterized by the trigger
threshold to be used. The computation of these curves for a group of indicators
then allows the selection of the best indicator the curve of which dominates
the curves of the other indicators. This methodology is illustrated using
indicators in the context of COVID-19 using deterministic compartmental models
in discrete-time, although the framework can be adapted for a larger class of
models.
