Optimal control on hybrid ODE Systems with application to a tick disease model | Zendy

Wandi Ding | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Optimal control on hybrid ODE Systems with application to a tick disease model

Author(s) -

Wandi Ding

Publication year - 2007

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2007.4.633

Subject(s) - ode , uniqueness , ordinary differential equation , optimal control , control theory (sociology) , state variable , tick , mathematics , variable (mathematics) , control variable , maximum principle , mathematical optimization , control (management) , differential equation , computer science , ecology , biology , mathematical analysis , statistics , artificial intelligence , physics , thermodynamics

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research