On a safety set for an epidemic model with a bounded population

Given a class of non-linear SIRS epidemic model, we analyse some useful conditions on the model parameters to determine a safety set for the containment of an epidemic. In addition, once that set is determined, we find control actions so that the epidemic remains within the security set with infecti...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 27; no. 2; pp. 263 - 281
Main Authors Coll, Carmen, Romero-Vivó, Sergio, Sánchez, Elena
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 27.04.2022
Subjects
Analysis
Apexes
control feedback
discrete-time non-linear system
Disease
Epidemics
epidemiological process
Epidemiology
Evolution
Farm buildings
Health aspects
Infection
Infections
Linear functions
Mathematical models
Population
positivity
Safety
Safety and security measures
stability
epidemiological process
control feedback
discrete-time non-linear system
positivity
stability
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ISSN1392-6292
1648-3510
DOI10.3846/mma.2022.14586

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Summary:Given a class of non-linear SIRS epidemic model, we analyse some useful conditions on the model parameters to determine a safety set for the containment of an epidemic. In addition, once that set is determined, we find control actions so that the epidemic remains within the security set with infection rates below an allowed amount. More specifically, for every initial state in a certain safety set of the state space there exists an adequate control policy maintaining the state of the system in such safety set. Sufficient conditions for the existence of a solution under a feedback are derived in terms of linear inequalities on the input vectors at the vertices of a polytope.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2022.14586