Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

1. Department of Mathematics, University of Tennessee, 1403 Circle Drive, Knoxville, TN 37996-1300

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 Metrics

Keywords hybrid system.; ordinary differential equations; tick disease; optimal control

Citation: Wandi Ding. Optimal control on hybrid ODE Systems with application to a tick disease model. Mathematical Biosciences and Engineering, 2007, 4(4): 633-659. doi: 10.3934/mbe.2007.4.633


This article has been cited by

  • 1. Milliward Maliyoni, Faraimunashe Chirove, Holly D. Gaff, Keshlan S. Govinder, A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence, Bulletin of Mathematical Biology, 2017, 79, 9, 1999, 10.1007/s11538-017-0317-y
  • 2. Holly D. Gaff, Elsa Schaefer, Suzanne Lenhart, Use of optimal control models to predict treatment time for managing tick-borne disease, Journal of Biological Dynamics, 2011, 5, 5, 517, 10.1080/17513758.2010.535910
  • 3. David Gammack, Elsa Schaefer, Holly Gaff, , Mathematical Concepts and Methods in Modern Biology, 2013, 105, 10.1016/B978-0-12-415780-4.00004-1
  • 4. Prasanta Kumar Mondal, T. K. Kar, Optimal treatment control and bifurcation analysis of a tuberculosis model with effect of multiple re-infections, International Journal of Dynamics and Control, 2017, 5, 2, 367, 10.1007/s40435-015-0176-z
  • 5. Christopher M. Baker, Target the Source: Optimal Spatiotemporal Resource Allocation for Invasive Species Control, Conservation Letters, 2017, 10, 1, 41, 10.1111/conl.12236
  • 6. Ludovic Mailleret, Valérie Lemesle, A note on semi-discrete modelling in the life sciences, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 367, 1908, 4779, 10.1098/rsta.2009.0153
  • 7. Milliward Maliyoni, Faraimunashe Chirove, Holly D. Gaff, Keshlan S. Govinder, A stochastic epidemic model for the dynamics of two pathogens in a single tick population, Theoretical Population Biology, 2019, 10.1016/j.tpb.2019.04.004
  • 8. Holly Gaff, Preliminary analysis of an agent-based model for a tick-borne disease, Mathematical Biosciences and Engineering, 2011, 8, 2, 463, 10.3934/mbe.2011.8.463

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved