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Abstract and Applied Analysis
Volume 2014, Article ID 263780, 14 pages
http://dx.doi.org/10.1155/2014/263780
Research Article

Mathematical Analysis of a General Two-Patch Model of Tuberculosis Disease with Lost Sight Individuals

1Department of Mathematics, Faculty of Science, University of Yaounde I, Yaounde 8390, Cameroon
2Department of Mathematics and Physics, National Advanced School of Engineering, University of Yaounde I, UMMISCO, Team Project GRIMCAPE, LIRIMA, Yaounde 8390, Cameroon
3Cheikh Anta Diop University, National Advanced School of Engineering, UMMISCO, 5085 Dakar, Senegal
4Department of Mathematics and Computer Science, Faculty of Science, University of Douala, UMMISCO, Team Project GRIMCAPE, LIRIMA, Douala 24157, Cameroon
5MaSIM Focus Area, North-West University, Mafikeng Campus, Mafikeng 2735, South Africa

Received 30 May 2014; Accepted 25 June 2014; Published 20 July 2014

Academic Editor: Abdon Atangana

Copyright © 2014 Abdias Laohombé 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.

Abstract

A two-patch model, ,   , is used to analyze the spread of tuberculosis, with an arbitrary number of latently infected compartments in each patch. A fraction of infectious individuals that begun their treatment will not return to the hospital for the examination of sputum. This fact usually occurs in sub-Saharan Africa, due to many reasons. The model incorporates migrations from one patch to another. The existence and uniqueness of the associated equilibria are discussed. A Lyapunov function is used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium is globally and asymptotically stable. When it is greater than one, there exists at least one endemic equilibrium. The local stability of endemic equilibria can be illustrated using numerical simulations. Numerical simulation results are provided to illustrate the theoretical results and analyze the influence of lost sight individuals.