Optimal Control on Hybrid ODE Systems with Application to a Tick Disease Model
by
Wandi Ding
Middle Tennessee State University

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.

Date received: August 20, 2007