Design of a vaccination law for an age-dependent epidemic model using state feedback

Candy Sonveaux; Joseph J. Winkin

doi:10.1016/j.ifacol.2022.10.378

Design of a vaccination law for an age-dependent epidemic model using state feedback

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Article dans les actes d'une conférence/un colloque

Résumé

An age-dependent epidemic model is studied with the goal of designing a state feedback stabilizing vaccination law to eradicate a disease. This model consists of a set of three nonlinear partial-integro differential equations (PIDE). A salient feature of the dynamical analysis is the fact that, if the basic reproduction number is greater than one, then the disease-free equilibrium is unstable. In view of this, we provide a linearizing state feedback vaccination law that is deduced from the one obtained for the PIDE model discretisation with respect to the age. Conditions guaranteeing stability of the closed-loop system and positivity of the feedback control are obtained using Isidori's theory and semigroup theory. Numerical simulations complete the analysis.

langue originale	Anglais
titre	Proceedings of the 4th IFAC Workshop CDDE 2022
Pages	65-70
Nombre de pages	6
Volume	55
Edition	26
Les DOIs	https://doi.org/10.1016/j.ifacol.2022.10.378
Etat de la publication	Publié - 2022
Evénement	4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022 - Kiel, Allemagne Durée: 7 sept. 2022 → 9 sept. 2022

Série de publications

Nom	IFAC-PapersOnLine
Editeur	IFAC Secretariat
ISSN (imprimé)	2405-8963

Une conférence

Une conférence	4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022
Pays/Territoire	Allemagne
La ville	Kiel
période	7/09/22 → 9/09/22

SDG des Nations Unies

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10.1016/j.ifacol.2022.10.378

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title = "Design of a vaccination law for an age-dependent epidemic model using state feedback",

abstract = "An age-dependent epidemic model is studied with the goal of designing a state feedback stabilizing vaccination law to eradicate a disease. This model consists of a set of three nonlinear partial-integro differential equations (PIDE). A salient feature of the dynamical analysis is the fact that, if the basic reproduction number is greater than one, then the disease-free equilibrium is unstable. In view of this, we provide a linearizing state feedback vaccination law that is deduced from the one obtained for the PIDE model discretisation with respect to the age. Conditions guaranteeing stability of the closed-loop system and positivity of the feedback control are obtained using Isidori's theory and semigroup theory. Numerical simulations complete the analysis.",

keywords = "(un)stability of equilibria, epidemiology, Infinite-dimensional systems, nonlinear control, partial integro-differential equations, positive systems",

author = "Candy Sonveaux and Winkin, {Joseph J.}",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.. All rights reserved.; 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022 ; Conference date: 07-09-2022 Through 09-09-2022",

year = "2022",

doi = "10.1016/j.ifacol.2022.10.378",

language = "English",

volume = "55",

series = "IFAC-PapersOnLine",

publisher = "IFAC Secretariat",

pages = "65--70",

booktitle = "Proceedings of the 4th IFAC Workshop CDDE 2022",

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}

Sonveaux, C & Winkin, JJ 2022, Design of a vaccination law for an age-dependent epidemic model using state feedback. Dans Proceedings of the 4th IFAC Workshop CDDE 2022. 26 edn, VOL. 55, IFAC-PapersOnLine, p. 65-70, 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022, Kiel, Allemagne, 7/09/22. https://doi.org/10.1016/j.ifacol.2022.10.378

Design of a vaccination law for an age-dependent epidemic model using state feedback. / Sonveaux, Candy ; Winkin, Joseph J.
Proceedings of the 4th IFAC Workshop CDDE 2022. Vol 55 26. Ed. 2022. p. 65-70 (IFAC-PapersOnLine).

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Article dans les actes d'une conférence/un colloque

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AU - Winkin, Joseph J.

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N2 - An age-dependent epidemic model is studied with the goal of designing a state feedback stabilizing vaccination law to eradicate a disease. This model consists of a set of three nonlinear partial-integro differential equations (PIDE). A salient feature of the dynamical analysis is the fact that, if the basic reproduction number is greater than one, then the disease-free equilibrium is unstable. In view of this, we provide a linearizing state feedback vaccination law that is deduced from the one obtained for the PIDE model discretisation with respect to the age. Conditions guaranteeing stability of the closed-loop system and positivity of the feedback control are obtained using Isidori's theory and semigroup theory. Numerical simulations complete the analysis.

AB - An age-dependent epidemic model is studied with the goal of designing a state feedback stabilizing vaccination law to eradicate a disease. This model consists of a set of three nonlinear partial-integro differential equations (PIDE). A salient feature of the dynamical analysis is the fact that, if the basic reproduction number is greater than one, then the disease-free equilibrium is unstable. In view of this, we provide a linearizing state feedback vaccination law that is deduced from the one obtained for the PIDE model discretisation with respect to the age. Conditions guaranteeing stability of the closed-loop system and positivity of the feedback control are obtained using Isidori's theory and semigroup theory. Numerical simulations complete the analysis.

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KW - Infinite-dimensional systems

KW - nonlinear control

KW - partial integro-differential equations

KW - positive systems

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Design of a vaccination law for an age-dependent epidemic model using state feedback

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