Identifiability and observability of the SIR model with quarantine

Frédéric Hamelin (1, 2) , Abderrahman Iggidr (3, 4) , Alain Rapaport (5) , Gauthier Sallet (3) , Max O Souza (6)

1 IGEPP - Institut de Génétique, Environnement et Protection des Plantes
2 Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement
3 IECL - Institut Élie Cartan de Lorraine
4 Inria Nancy - Grand Est
5 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
6 Instituto de Matematica [Fluminense]

We analyze the identifiability and observability of the well-known SIR epidemic model with an additional compartment Q of the sub-population of infected individuals that are placed in quarantine (SIQR model), considering that the flow of individuals placed in quarantine and the size of the quarantine population are known at any time. Then, we focus on the problem of identification of the model parameters, with the synthesis of an observer.

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Frédéric Hamelin, Abderrahman Iggidr, Alain Rapaport, Gauthier Sallet, Max O Souza. Identifiability and observability of the SIR model with quarantine. 2021. ⟨hal-03160829v1⟩