%0 Journal Article
%T A Mathematical Model for the Transmission and Spread of Drug Sensitive and Resistant Malaria Strains within a Human Population
%A Julius Tumwiine
%A Senelani D. Hove-Musekwa
%A Farai Nyabadza
%J ISRN Biomathematics
%D 2014
%R 10.1155/2014/636973
%X 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. 1. istant parasites, and temporary immune humans and Introduction Malaria is one of the most devastating infectious diseases in the world, infecting approximately 300¨C500 million people annually worldwide, resulting in over a million deaths [1, 2]. The 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. There 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. After 1-2 weeks the schizont ruptures and releases the merozoites into the blood stream which then invade the red blood cells. The clinical symptoms of malaria are due to the rupture of the red blood cells and release of the parasitesĄŻ waste and cellsĄŻ debris into the blood stream. After several asexual cycles, some of the merozoites invade red blood
%U http://www.hindawi.com/journals/isrn.biomathematics/2014/636973/