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

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution

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.

Original language	English
Title of host publication	Proceedings of the 4th IFAC Workshop CDDE 2022
Pages	65-70
Number of pages	6
Volume	55
Edition	26
DOIs	https://doi.org/10.1016/j.ifacol.2022.10.378
Publication status	Published - 2022
Event	4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022 - Kiel, Germany Duration: 7 Sept 2022 → 9 Sept 2022

Publication series

Name	IFAC-PapersOnLine
Publisher	IFAC Secretariat
ISSN (Print)	2405-8963

Conference

Conference	4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022
Country/Territory	Germany
City	Kiel
Period	7/09/22 → 9/09/22

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

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

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10.1016/j.ifacol.2022.10.378

Cite this

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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",

edition = "26",

}

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

TY - GEN

T1 - Design of a vaccination law for an age-dependent epidemic model using state feedback

AU - Sonveaux, Candy

AU - Winkin, Joseph J.

PY - 2022

Y1 - 2022

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.

KW - (un)stability of equilibria

KW - epidemiology

KW - Infinite-dimensional systems

KW - nonlinear control

KW - partial integro-differential equations

KW - positive systems

UR - https://www.scopus.com/pages/publications/85145438439

U2 - 10.1016/j.ifacol.2022.10.378

DO - 10.1016/j.ifacol.2022.10.378

M3 - Conference contribution

AN - SCOPUS:85145438439

VL - 55

T3 - IFAC-PapersOnLine

SP - 65

EP - 70

BT - Proceedings of the 4th IFAC Workshop CDDE 2022

T2 - 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022

Y2 - 7 September 2022 through 9 September 2022

ER -

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

Abstract

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UN SDGs

Keywords

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