Nonlinear Dynamics

, Volume 61, Issue 4, pp 729–748 | Cite as

Optimal control of the transmission dynamics of tuberculosis

Original Paper


This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A tuberculosis model which incorporates the essential biological and epidemiological features of the disease such as exogenous reinfection and chemoprophylaxis of latently infected individuals, and treatment of the infectious is developed and rigorously analyzed. Based on this continuous model, the tuberculosis control is formulated and solved as an optimal control theory problem, indicating how a control term on the chemoprophylaxis should be introduced in the population to reduce the number of individuals with active TB. The feedback control law has been proved to be capable of reducing the number of individuals with active TB. An advantage is that the proposed scheme accounts for the energy wasted by the controller and the closed-loop performance on tracking. Numerical results show the performance of the optimization strategy.


Epidemiological models Tuberculosis Optimal control Riccati equation 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of ScienceUniversity of DoualaDoualaCameroon

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