Title :

Nonlinear adaptive observers for SIS system with primary infections

Author(s) :

Fang, Marcel [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Compréhension mathématique multi-échelles d’écosystèmes vivants complexes avec structures émergentes [MUSCLEES]
Bliman, Pierre-Alexandre [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Compréhension mathématique multi-échelles d’écosystèmes vivants complexes avec structures émergentes [MUSCLEES]
Efimov, Denis [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Finite-time control and estimation for distributed systems [VALSE]
Ushirobira, Rosane [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Finite-time control and estimation for distributed systems [VALSE]

English keyword(s) :

Adaptive estimation
SIS model
Lyapunov method
Mathematical epidemiology

HAL domain(s) :

Sciences de l'ingénieur [physics]/Automatique / Robotique
Sciences du Vivant [q-bio]/Santé publique et épidémiologie

English abstract : [en]

Observation and identification are crucially important for the practical use of compartmental models in epidemiology. Typically, the state and parameters of the epidemic model are evaluated based on the number of infected ...
Show more >Observation and identification are crucially important for the practical use of compartmental models in epidemiology. Typically, the state and parameters of the epidemic model are evaluated based on the number of infected individuals (prevalence) or the newly infected cases per time unit (incidence). However, when reinfections are possible, additional data such as the number of primary infections are retrievable. In this note, we investigate whether measuring the number of primary infections can improve estimation. To do so, we present several nonlinear adaptive observers for a simple infection model with waning immunity and subsequent reinfections. We then prove the practical asymptotic stability of the estimation errors using the Lyapunov function method. Finally, we illustrate the efficacy of the observers via simulations.Show less >

Language :

Anglais

ANR Project :

Nouvelles questions d'observation et de commande motivées par l'Epidémiologie

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL