Table of Contents
ISRN Biomathematics
Volume 2014, Article ID 636973, 12 pages
http://dx.doi.org/10.1155/2014/636973
Research Article

A Mathematical Model for the Transmission and Spread of Drug Sensitive and Resistant Malaria Strains within a Human Population

1Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410, Mbarara, Uganda
2Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC 939, Ascot, Bulawayo, Zimbabwe
3Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa

Received 18 February 2014; Accepted 12 March 2014; Published 16 April 2014

Academic Editors: J. Chow and J. Suehnel

Copyright © 2014 Julius Tumwiine 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

Malaria remains by far the world's most important tropical disease, killing more people than any other communicable disease. A number of preventive and control measures have been put in place and most importantly drug treatment. The emergence of drug resistance against the most common and affordable antimalarials is widespread and poses a key obstacle to malaria control. A mathematical model that incorporates evolution of drug resistance and treatment as a preventive strategy is formulated and analyzed. The qualitative analysis of the model is given in terms of the effective reproduction number, . The existence and stability of the disease-free and endemic equilibria of the model are studied. We establish the threshold parameters below which the burden due to malaria can be brought under control. Numerical simulations are done to determine the role played by key parameters in the model. The public health implications of the results are twofold; firstly every effort should be taken to minimize the evolution of drug resistance due to treatment failure and secondly high levels of treatment and development of immunity are essential in reducing the malaria burden.