Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 398476, 12 pages
Research Article

Optimal Control of the Lost to Follow Up in a Tuberculosis Model

Laboratory of Applied Mathematics, University of Yaoundé 1, P.O. Box 812, Yaounde, Cameroon

Received 28 April 2011; Revised 23 June 2011; Accepted 22 July 2011

Academic Editor: Thierry Busso

Copyright © 2011 Yves Emvudu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the problem of optimal control for the transmission dynamics of tuberculosis (TB). A TB model that considers the existence of a new class (mainly in the African context) is considered: the lost to follow up individuals. Based on the model formulated and studied in the work of Plaire Tchinda Mouofo, (2009), the TB control is formulated and solved as an optimal control theory problem using the Pontryagin's maximum principle (Pontryagin et al., 1992). This control strategy indicates how the control of the lost to follow up class can considerably influence the basic reproduction ratio so as to reduce the number of lost to follow up. Numerical results show the performance of the optimization strategy.