Geometric approach for non pharmaceutical interventions in epidemiology

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 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.