Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth
In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control prob...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018022 |
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| author | Markus Thäter Kurt Chudej Hans Josef Pesch |
| author_facet | Markus Thäter Kurt Chudej Hans Josef Pesch |
| author_sort | Markus Thäter |
| collection | DOAJ |
| description | In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions. |
| format | Article |
| id | doaj-art-9fa8dda9c0bc490aad663be14c4702c8 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9fa8dda9c0bc490aad663be14c4702c82025-01-24T02:40:44ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-03-0115248550510.3934/mbe.2018022Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growthMarkus Thäter0Kurt Chudej1Hans Josef Pesch2Chair of Mathematics in Engineering Sciences, University of Bayreuth, Bayreuth, D 95440, GermanyChair of Mathematics in Engineering Sciences, University of Bayreuth, Bayreuth, D 95440, GermanyChair of Mathematics in Engineering Sciences, University of Bayreuth, Bayreuth, D 95440, GermanyIn this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions.https://www.aimspress.com/article/doi/10.3934/mbe.2018022seir modellogistic growthinfectious diseasesoptimal controlvaccination strategyverification of numerical results |
| spellingShingle | Markus Thäter Kurt Chudej Hans Josef Pesch Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth Mathematical Biosciences and Engineering seir model logistic growth infectious diseases optimal control vaccination strategy verification of numerical results |
| title | Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth |
| title_full | Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth |
| title_fullStr | Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth |
| title_full_unstemmed | Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth |
| title_short | Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth |
| title_sort | optimal vaccination strategies for an seir model of infectious diseases with logistic growth |
| topic | seir model logistic growth infectious diseases optimal control vaccination strategy verification of numerical results |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018022 |
| work_keys_str_mv | AT markusthater optimalvaccinationstrategiesforanseirmodelofinfectiousdiseaseswithlogisticgrowth AT kurtchudej optimalvaccinationstrategiesforanseirmodelofinfectiousdiseaseswithlogisticgrowth AT hansjosefpesch optimalvaccinationstrategiesforanseirmodelofinfectiousdiseaseswithlogisticgrowth |