A novel control set-valued approach with application to epidemic models
type: Item
instance of: scholarly article
title: A novel control set-valued approach with application to epidemic models
zbMATH Open document ID: 1478.92179
author: L. Boujallal
author: Mohamed Elhia
author: Omar Balatif
published in: Journal of Applied Mathematics and Computing
publication date: 2021-11-29T00:00:00Z
review text: This paper studies an approach to characterize one or more controls to achieve the null number of infected population at a final time. The epidemic model is described as \(\dot{x}=f(x,y,u)\) and \(\dot{y}=\psi(x,y,u)\), where \(x=(x_1,\cdots,x_n)\) with each component positive indicates the numbers of individuals in a population such as susceptible and recovered and \(y\), which is positive, denotes the number of infected individuals. The control \(u\) takes values in a bounded constraints subset. Here \(f\) can be non-affine with respect to the control and the dynamics \(\psi\) rely on the control variable. Based on the viability theory, the paper finds the control \(u\) such that the solution of the system is confined in a region while the number of infected individuals dies out eventually. Control set-valued approaches have been used and the existence of continuous selections under sufficient conditions has been tackled. An application to SIRS compartmental model is also provided.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 7435173
zbMATH Keywords: nonlinear control systems
zbMATH Keywords: epidemic models
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: viability theory
zbMATH Keywords: contingent cone
zbMATH Keywords: selections
MaRDI profile type: Publication
full work available at URL: s12190-020-01392-x
OpenAlex ID: W3043458211
Wikidata QID: Q98662281
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DOI: 10.1007/S12190-020-01392-X
description: scientific article; zbMATH DE number 7435173