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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-07-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.633 |
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| Summary: | 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. |
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| ISSN: | 1551-0018 |