Table of Contents
ISRN Biomathematics
Volume 2012 (2012), Article ID 459829, 20 pages
Research Article

Modelling the Role of Diagnosis, Treatment, and Health Education on Multidrug-Resistant Tuberculosis Dynamics

1Department of Mathematical Sciences, University of Malawi, Chancellor College, P. O. Box 280, Zomba, Malawi
2Department of Mathematics and Statistics, University of Malawi, The Polytechnic, Private Bag 303, Chichiri, Blantyre 3, Malawi
3Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC 939 Ascot, Bulawayo, Zimbabwe
4Mathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, Tanzania

Received 2 April 2012; Accepted 13 May 2012

Academic Editors: J. R. C. Piqueira, M. Santillán, and J. Tabak

Copyright © 2012 M. Maliyoni 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.


Tuberculosis, an airborne disease affecting almost a third of the world’s population remains one of the major public health burdens globally, and the resurgence of multidrug-resistant tuberculosis in some parts of sub-Saharan Africa calls for concern. To gain insight into its qualitative dynamics at the population level, mathematical modeling which require as inputs key demographic and epidemiological information can fill in gaps where field and lab data are not readily available. A deterministic model for the transmission dynamics of multi-drug resistant tuberculosis to assess the impact of diagnosis, treatment, and health education is formulated. The model assumes that exposed individuals develop active tuberculosis due to endogenous activation and exogenous re-infection. Treatment is offered to all infected individuals except those latently infected with multi-drug resistant tuberculosis. Qualitative analysis using the theory of dynamical systems shows that, in addition to the disease-free equilibrium, there exists a unique dominant locally asymptotically stable equilibrium corresponding to each strain. Numerical simulations suggest that, at the current level of control strategies (with Malawi as a case study), the drug-sensitive tuberculosis can be completely eliminated from the population, thereby reducing multi-drug resistant tuberculosis.