Dynamical analysis and feedback control of age-structured epidemic models

Résumé

The field of epidemiology concerns notably the study of the distribution of diseases (in terms of location, occurrence and characteristics) and the study of the health states of a given population. But il also relies on such analysis for the control of health problems. The first part can be dealt with mathematical modeling whereas the second part benefits from advances in the field of control theory. In this work, both subjects are tackled. Firstly, a case study concerning the covid-19 disease is performed thanks to a nonlinear SIRD model described by ordinary differential equations. The dynamical analysis of this model is developed to ensure the quality of the model (well-posedness) and to provide prediction for the future (stability). Then two vaccination strategies are proposed in order to imply disease eradication, by using two methods of control theory: observer-based output feedback design and model predictive control. Secondly, a nonlinear SIR model described by partial integro-differential equations is studied. This model is well-suited to describe the evolution of long-term diseases. Results concerning the dynamical analysis of the model in terms of existence and uniqueness of solution, nonnegativity of the state variables and stability are established. In view of the stability results, a control law is needed to obtain disease eradication. An innovative extension of the linearizing state feedback approach is given for the infinite-dimensional case to obtain a stabilizing vaccination law whose properties are proven.

la date de réponse	19 déc. 2023
langue originale	Anglais
L'institution diplômante	Universite de Namur
Superviseur	Joseph Winkin (Promoteur), Timoteo Carletti (Président), M. Elarbi Achhab (Jury), Amaury Hayat (Jury), Alexandre Mauroy (Jury) & Christophe Prieur (Jury)