Sufficient optimality conditions for a class of epidemic problems with control on the boundary
In earlier paper of V. Capasso et al it is considered a simply model of controlling an epidemic, which is described by three functionals and systems of two PDE equations having the feedback operator on the boundary. Necessary optimality conditions and two gradient-type algorithms are derived. This p...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2016-12-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017017 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590075497545728 |
|---|---|
| author | Miniak-Górecka Alicja Nowakowski Andrzej |
| author_facet | Miniak-Górecka Alicja Nowakowski Andrzej |
| author_sort | Miniak-Górecka Alicja |
| collection | DOAJ |
| description | In earlier paper of V. Capasso et al it is considered a simply model of controlling an epidemic, which is described by three functionals and systems of two PDE equations having the feedback operator on the boundary. Necessary optimality conditions and two gradient-type algorithms are derived. This paper constructs dual dynamic programming method to derive sufficient optimality conditions for optimal solution as well $\varepsilon $-optimality conditions in terms of dual dynamic inequalities. Approximate optimality and numerical calculations are presented too. |
| format | Article |
| id | doaj-art-bc6b1e3051f04db6b3273d067578773c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-bc6b1e3051f04db6b3273d067578773c2025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-12-0114126327510.3934/mbe.2017017Sufficient optimality conditions for a class of epidemic problems with control on the boundaryMiniak-Górecka Alicja0Nowakowski Andrzej1Faculty of Math and Computer Sciences, University of Lodz, Banacha 22, 90-238 Lodz, PolandFaculty of Math and Computer Sciences, University of Lodz, Banacha 22, 90-238 Lodz, PolandIn earlier paper of V. Capasso et al it is considered a simply model of controlling an epidemic, which is described by three functionals and systems of two PDE equations having the feedback operator on the boundary. Necessary optimality conditions and two gradient-type algorithms are derived. This paper constructs dual dynamic programming method to derive sufficient optimality conditions for optimal solution as well $\varepsilon $-optimality conditions in terms of dual dynamic inequalities. Approximate optimality and numerical calculations are presented too.https://www.aimspress.com/article/doi/10.3934/mbe.2017017sufficient optimality conditionsdual dynamic programmingdual dynamic programmingepidemic problemparabolic equation |
| spellingShingle | Miniak-Górecka Alicja Nowakowski Andrzej Sufficient optimality conditions for a class of epidemic problems with control on the boundary Mathematical Biosciences and Engineering sufficient optimality conditions dual dynamic programming dual dynamic programming epidemic problem parabolic equation |
| title | Sufficient optimality conditions for a class of epidemic problems with control on the boundary |
| title_full | Sufficient optimality conditions for a class of epidemic problems with control on the boundary |
| title_fullStr | Sufficient optimality conditions for a class of epidemic problems with control on the boundary |
| title_full_unstemmed | Sufficient optimality conditions for a class of epidemic problems with control on the boundary |
| title_short | Sufficient optimality conditions for a class of epidemic problems with control on the boundary |
| title_sort | sufficient optimality conditions for a class of epidemic problems with control on the boundary |
| topic | sufficient optimality conditions dual dynamic programming dual dynamic programming epidemic problem parabolic equation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017017 |
| work_keys_str_mv | AT miniakgoreckaalicja sufficientoptimalityconditionsforaclassofepidemicproblemswithcontrolontheboundary AT nowakowskiandrzej sufficientoptimalityconditionsforaclassofepidemicproblemswithcontrolontheboundary |