Identifiability and Observability in Epidemiological Models - a survey -

Observabilité, Identifiabilité et Epidémiologie

Nik Cunniffe (1) , Frédéric Hamelin (2) , Abderrahman Iggidr (3, 4) , Alain Rapaport (5) , Gauthier Sallet (4)

1 CAM - University of Cambridge [UK]
2 Institut Agro Rennes Angers
3 Inria Nancy - Grand Est
4 IECL - Institut Élie Cartan de Lorraine
5 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

In this review, we recall the concepts of Identifiability and Observability of dynamical systems, and analyse them in the framework of Mathematical Epidemiology. We show that, even for simple and well known models of the literature, these properties are not always fulfilled. We then consider the problem of practical identifiability and observability, which are connected to sensitivity and numerical condition numbers. We also recall the concept of observers to reconstruct state variable of the model which are not observed, and show how it can used with epidemiological models.

Mots clés: Dynamical systems; Identifiability; Observability; Mathematical Epidemiology; Sensitivity Analysis

Domaines: Systèmes dynamiques [math.DS]; Modélisation et simulation; Optimisation et contrôle [math.OC]; Sciences du Vivant [q-bio]; Santé publique et épidémiologie

Nik Cunniffe, Frédéric Hamelin, Abderrahman Iggidr, Alain Rapaport, Gauthier Sallet. Identifiability and Observability in Epidemiological Models - a survey -. 2023. ⟨hal-02995562v3⟩