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

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

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 P...

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Main Authors: Yves Emvudu, Ramsès Demasse, Dany Djeudeu
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Computational and Mathematical Methods in Medicine
Online Access:http://dx.doi.org/10.1155/2011/398476
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spelling doaj-0476d8d2623b447ca21193513ee5dbd42020-11-24T21:17:03ZengHindawi LimitedComputational and Mathematical Methods in Medicine1748-670X1748-67182011-01-01201110.1155/2011/398476398476Optimal Control of the Lost to Follow Up in a Tuberculosis ModelYves Emvudu0Ramsès Demasse1Dany Djeudeu2Laboratory of Applied Mathematics, University of Yaoundé 1, P.O. Box 812, Yaounde, CameroonLaboratory of Applied Mathematics, University of Yaoundé 1, P.O. Box 812, Yaounde, CameroonLaboratory of Applied Mathematics, University of Yaoundé 1, P.O. Box 812, Yaounde, CameroonThis 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.http://dx.doi.org/10.1155/2011/398476
collection DOAJ
language English
format Article
sources DOAJ
author Yves Emvudu
Ramsès Demasse
Dany Djeudeu
spellingShingle Yves Emvudu
Ramsès Demasse
Dany Djeudeu
Optimal Control of the Lost to Follow Up in a Tuberculosis Model
Computational and Mathematical Methods in Medicine
author_facet Yves Emvudu
Ramsès Demasse
Dany Djeudeu
author_sort Yves Emvudu
title Optimal Control of the Lost to Follow Up in a Tuberculosis Model
title_short Optimal Control of the Lost to Follow Up in a Tuberculosis Model
title_full Optimal Control of the Lost to Follow Up in a Tuberculosis Model
title_fullStr Optimal Control of the Lost to Follow Up in a Tuberculosis Model
title_full_unstemmed Optimal Control of the Lost to Follow Up in a Tuberculosis Model
title_sort optimal control of the lost to follow up in a tuberculosis model
publisher Hindawi Limited
series Computational and Mathematical Methods in Medicine
issn 1748-670X
1748-6718
publishDate 2011-01-01
description 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.
url http://dx.doi.org/10.1155/2011/398476
work_keys_str_mv AT yvesemvudu optimalcontrolofthelosttofollowupinatuberculosismodel
AT ramsesdemasse optimalcontrolofthelosttofollowupinatuberculosismodel
AT danydjeudeu optimalcontrolofthelosttofollowupinatuberculosismodel
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