  Various non pharmaceutical interventions have been settled to minimise the
burden of the COVID-19 outbreak. We build a framework to analyse the dynamics
of non pharmaceutical interventions, to distinguish between mitigations
measures leading to objective scientific improvements and mitigations based on
both political and scientific considerations. We analyse two possible
strategies within this framework. Namely, we consider mitigations driven by the
limited resources of the health system and mitigations where a constant set of
measures is applied at different moments. We describe the optimal interventions
for these scenarios. Our approach is mathematical and involves sir differential
systems, it is qualitative and geometrical rather than computational. Along
with the analysis of these scenarios, we collect several results that may be
useful on their own, in particular on the ground when the variables are not
known in real time.
