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 infect...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2022-04-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://tede.vgtu.lt/index.php/MMA/article/view/14586 |
| _version_ | 1818479293262462976 |
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| author | Carmen Coll Sergio Romero-Vivó Elena Sánchez |
| author_facet | Carmen Coll Sergio Romero-Vivó Elena Sánchez |
| author_sort | Carmen Coll |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-12-10T09:58:53Z |
| format | Article |
| id | doaj.art-93b49472c3104518bf844aaf569e0dd3 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-10T09:58:53Z |
| publishDate | 2022-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-93b49472c3104518bf844aaf569e0dd32022-12-22T01:53:24ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102022-04-0127210.3846/mma.2022.14586On a safety set for an epidemic model with a bounded populationCarmen Coll0Sergio Romero-Vivó1Elena Sánchez2Institut Universitari de Matemàtica Multidisciplinar, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, SpainInstitut Universitari de Matemàtica Multidisciplinar, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, SpainInstitut Universitari de Matemàtica Multidisciplinar, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, Spain 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. https://tede.vgtu.lt/index.php/MMA/article/view/14586epidemiological processdiscrete-time non-linear systempositivitystabilitycontrol feedback |
| spellingShingle | Carmen Coll Sergio Romero-Vivó Elena Sánchez On a safety set for an epidemic model with a bounded population Mathematical Modelling and Analysis epidemiological process discrete-time non-linear system positivity stability control feedback |
| title | On a safety set for an epidemic model with a bounded population |
| title_full | On a safety set for an epidemic model with a bounded population |
| title_fullStr | On a safety set for an epidemic model with a bounded population |
| title_full_unstemmed | On a safety set for an epidemic model with a bounded population |
| title_short | On a safety set for an epidemic model with a bounded population |
| title_sort | on a safety set for an epidemic model with a bounded population |
| topic | epidemiological process discrete-time non-linear system positivity stability control feedback |
| url | https://tede.vgtu.lt/index.php/MMA/article/view/14586 |
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