Elementary formulae for social distancing scenarios: Application to COVID-19 mitigation via feedback control

Michel Fliess (1, 2) , Cédric Join (3, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 AL.I.E.N. - ALgèbre pour Identification & Estimation Numériques
3 CRAN - Centre de Recherche en Automatique de Nancy

Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields elementary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the number of uninfected people may be taken into account. Those formulae might therefore be useful to decision makers. A feedback loop stemming from model-free control leads to a remarkable robustness with respect to severe uncertainties of various kinds. Although an identification procedure is presented, a good knowledge of the recovery rate is not necessary for our control strategy. Several convincing computer experiments are displayed.

Mots clés: biomedical control; COVID-19; social distancing; SIR model; nonlinear feedback control; flatness-based control; model-free control; robustness; identifiability; algebraic differentiator

Domaines: Santé publique et épidémiologie; Systèmes et contrôle [cs.SY]; Automatique; Optimisation et contrôle [math.OC]

Michel Fliess, Cédric Join. Elementary formulae for social distancing scenarios: Application to COVID-19 mitigation via feedback control. 2021. ⟨hal-03414354⟩