Research Article A Mathematical Model for the Transmission and Spread of Drug Sensitive and Resistant Malaria Strains within a Human Population Julius Tumwiine, 1 Senelani D. Hove-Musekwa, 2 and Farai Nyabadza 3 1 Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410, Mbarara, Uganda 2 Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC 939, Ascot, Bulawayo, Zimbabwe 3 Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa Correspondence should be addressed to Farai Nyabadza; f.nyaba@gmail.com 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. Tis 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. 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. Te emergence of drug resistance against the most common and afordable 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. Te qualitative analysis of the model is given in terms of the efective reproduction number, √   . Te 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. Te public health implications of the results are twofold; frstly every efort 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. 1. Introduction Malaria is one of the most devastating infectious diseases in the world, infecting approximately 300–500 million people annually worldwide, resulting in over a million deaths [1, 2]. Te high risk groups include young children, pregnant women, and nonimmune travelers to malarious regions. It is reported that one child dies every 30 seconds from this disease. Malaria is caused by Plasmodium parasites. Tere are 4 main types: Plasmodium vivax, Plasmodium ovale, Plasmodium malaria, and Plasmodium falciparum. It is the Plasmodium falciparum that causes most of the severe diseases and deaths and is most prevalent in Africa [3]. Malaria parasites are transferred by female Anopheles mosquitoes while they bite humans for a blood meal for the development of their eggs. During the blood meal, the mosquito injects sporozoites into the blood stream. In few minutes, the sporozoites enter the liver cells where each sporozoite develops into a tissue schizont that contains 10,000 to 30,000 merozoites. Afer 1-2 weeks the schizont ruptures and releases the merozoites into the blood stream which then invade the red blood cells. Te clinical symptoms of malaria are due to the rupture of the red blood cells and release of the parasites’ waste and cells’ debris into the blood stream. Afer several asexual cycles, some of the merozoites invade red blood cells and there develop into either male or female gametocytes. When a female mosquito bites an infected person, it ingests blood containing male and female gametocytes. Tese may be transmitted to another human host during the mosquito’s next blood meal. Te viable Hindawi Publishing Corporation ISRN Biomathematics Volume 2014, Article ID 636973, 12 pages http://dx.doi.org/10.1155/2014/636973