title: Optimal control on hybrid ode systems with application to a tick disease model.
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.
authors.affiliation: Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN 37996-1300, USA. ding@math.utk.edu
authors.forename: Wandi
authors.initials: W
authors.lastname: Ding
mesh_terms: D000818:Animals; D003670:Deer / Q000469:parasitology*; D006801:Humans; D007306:Insecticides / Q000494:pharmacology; D007558:Italy; D018884:Ixodes / Q000254:growth & development* / Q000382:microbiology; D008193:Lyme Disease / Q000382:microbiology / Q000517:prevention & control / Q000635:transmission* / Q000662:veterinary*; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics; D011720:Pyrazoles / Q000494:pharmacology; D012621:Seasons; D017282:Tick-Borne Diseases / Q000382:microbiology / Q000517:prevention & control / Q000635:transmission* / Q000662:veterinary*
chemical_list: D007306:Insecticides; D011720:Pyrazoles; C082360:fipronil