Optimal Control Strategies of a Tuberculosis Model with Exogenous Reinfection

  • Yali Yang
  • Xiuchao Song
  • Yuzhou Wang
  • Guoyun Luo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)


For the tuberculosis (TB) model with exogenous reinfection, we study the impact of two control strategies: chemoprophylaxis and treatment. We focus primarily on controlling the disease using an objective function based on a combination of minimizing the number of TB infections and minimizing the cost of control strategies. By using Pontryagin’s Maximum Principle, we derive the optimal levels of the two controls. Numerical simulations of the optimal system indicate that the strategies should be improved as the exogenous reinfection transmission coefficient increasing.


tuberculosis model exogenous reinfection optimal control pontryagin’s Maximum Principle 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yali Yang
    • 1
    • 2
  • Xiuchao Song
    • 2
  • Yuzhou Wang
    • 2
  • Guoyun Luo
    • 3
  1. 1.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina
  2. 2.College of ScienceAir Force Engineering UniversityXi’anChina
  3. 3.Unit 94170 of the PLAXi’anChina

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