Optimal control on hybrid ODE Systems with application to a tick disease model
We are considering an optimal control problem for a type of hybrid system involving ordinary differentialequations and a discrete time feature. One state variable hasdynamics in only one season of the year and has a jump conditionto obtain the initial condition for that corresponding season inthe ne...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2007-07-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.633 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590187363827712 |
|---|---|
| author | Wandi Ding |
| author_facet | Wandi Ding |
| author_sort | Wandi Ding |
| collection | DOAJ |
| description | We are considering an optimal control problem for a type of hybrid system involving ordinary differentialequations and a discrete time feature. One state variable hasdynamics in only one season of the year and has a jump conditionto obtain the initial condition for that corresponding season inthe next year. The other state variable has continuous dynamics.Given a general objective functional, existence, necessaryconditions and uniqueness for an optimal control are established.We apply our approach to a tick-transmitted disease model with agestructure in which the tick dynamics changes seasonally whilehosts have continuous dynamics. The goal is to maximizedisease-free ticks and minimize infected ticks through an optimalcontrol strategy of treatment with acaricide. Numerical examplesare given to illustrate the results. |
| format | Article |
| id | doaj-art-5dfcf52587ed4a46ae80b6d19fb62246 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5dfcf52587ed4a46ae80b6d19fb622462025-01-24T01:54:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-07-014463365910.3934/mbe.2007.4.633Optimal control on hybrid ODE Systems with application to a tick disease modelWandi Ding0Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN 37996-1300We are considering an optimal control problem for a type of hybrid system involving ordinary differentialequations and a discrete time feature. One state variable hasdynamics in only one season of the year and has a jump conditionto obtain the initial condition for that corresponding season inthe next year. The other state variable has continuous dynamics.Given a general objective functional, existence, necessaryconditions and uniqueness for an optimal control are established.We apply our approach to a tick-transmitted disease model with agestructure in which the tick dynamics changes seasonally whilehosts have continuous dynamics. The goal is to maximizedisease-free ticks and minimize infected ticks through an optimalcontrol strategy of treatment with acaricide. Numerical examplesare given to illustrate the results.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.633hybridsystem.ordinary differential equationstick diseaseoptimal control |
| spellingShingle | Wandi Ding Optimal control on hybrid ODE Systems with application to a tick disease model Mathematical Biosciences and Engineering hybridsystem. ordinary differential equations tick disease optimal control |
| title | Optimal control on hybrid ODE Systems with application to a tick disease model |
| title_full | Optimal control on hybrid ODE Systems with application to a tick disease model |
| title_fullStr | Optimal control on hybrid ODE Systems with application to a tick disease model |
| title_full_unstemmed | Optimal control on hybrid ODE Systems with application to a tick disease model |
| title_short | Optimal control on hybrid ODE Systems with application to a tick disease model |
| title_sort | optimal control on hybrid ode systems with application to a tick disease model |
| topic | hybridsystem. ordinary differential equations tick disease optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.633 |
| work_keys_str_mv | AT wandiding optimalcontrolonhybridodesystemswithapplicationtoatickdiseasemodel |