%0 Journal Article %1 Ding2007 %A Ding, Wandi %D 2007 %J Mathematical Biosciences and Engineering %K Ixodes Animals model borrelia Pyrazoles Tick-BorneDiseases parasitology LymeDisease Humans mathematical PopulationDynamics pharmacology Italy Models growth/&/development/microbiology microbiology/prevention/&/control/transmission/veterinary NumericalAnalysis Insecticides Seasons Biological Computer-Assisted Deer %N 4 %P 633--659 %R 10.1267/science.040579197 %T Optimal control on hybrid ode systems with application to a tick disease model. %U http://dx.doi.org/10.1267/science.040579197 %V 4 %X We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a tick-transmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.

@article{Ding2007, abstract = {We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a tick-transmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.}, added-at = {2010-01-14T17:43:53.000+0100}, author = {Ding, Wandi}, biburl = {https://www.bibsonomy.org/bibtex/2290eb8cc9d95633026f3f0becb9baa83/uvesco}, doi = {10.1267/science.040579197}, file = {:Ding2007.pdf:PDF}, institution = {Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN 37996-1300, USA. ding@math.utk.edu}, interhash = {a29e8fee989105c6bda7dd41013d1e5f}, intrahash = {290eb8cc9d95633026f3f0becb9baa83}, journal = {Mathematical Biosciences and Engineering}, keywords = {Ixodes Animals model borrelia Pyrazoles Tick-BorneDiseases parasitology LymeDisease Humans mathematical PopulationDynamics pharmacology Italy Models growth/&/development/microbiology microbiology/prevention/&/control/transmission/veterinary NumericalAnalysis Insecticides Seasons Biological Computer-Assisted Deer}, language = {eng}, medline-pst = {ppublish}, month = Oct, note = {EFSA}, number = 4, pages = {633--659}, pii = {040579197}, pmid = {17924716}, timestamp = {2010-01-14T17:43:53.000+0100}, title = {Optimal control on hybrid ode systems with application to a tick disease model.}, url = {http://dx.doi.org/10.1267/science.040579197}, volume = 4, year = 2007 }