Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol.4, No.10, 2014 27 An Epidemiological Model of Malaria at Techiman Municipality, Ghana Isaac Kwasi Adu (Corresponding author) Department of Mathematics, Valley View University, Techiman Campus, P. O. Box 183 B/A-Ghana Tel: +233-244584704 E-mail: ikeadu_74@yahoo.com Douglas Kwasi Boah Department of Mathematics, University for Development Studies P. O. Box 24 Navrongo-Ghana Tel: +233-243676263 E-mail: boahdouglas@yahoo.com Francis Julius Gyebil Mathematics & Statistics Department, Kumasi Polytechnic, Ghana P. O. Box 854 Kumasi-Ghana Tel: +233-244742747 E-mail:gyebilk70@yahoo.com Abstract The study examined the prevalence of Malaria in the Techiman Municipality of Ghana. We used model to analyze, model and predict the prevalence of Malaria disease in the municipality. The study is made up of two sections. An model without the vital dynamics and an with vital dynamics were used to explain the spread of the Malaria in the Techiman Municipality followed by the Fred Brauer simple treatment model ( ) to determine whether the treatment of malaria in the municipality is beneficial. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium states respectively. The stability condition of each equilibrium point is discussed. The basic reproductive number of Malaria without the vital dynamics is estimated to be and the basic reproductive number of Malaria with the vital dynamics is estimated to be in the Techiman Municipality. The basic reproductive numbers of the model and the modified malaria model were also estimated to be and respectively. Our work shows that the reproductive number ( ) of Malaria infection at Techiman Municipality is less than 1( ). Our work also shows that malaria treatment is beneficial in the municipality. According to the results of this study whenever the transmission rate coefficient in any of the models is increased, , but when the transmission rate coefficient is reduced, . We recommend that Malaria control measures should be intensified in the municipality so as to decrease the rate of transmission. Keywords: SIRS model, Stability analysis, Equilibrium points, Mathematical model, Epidemiological model. 1. Introduction Malaria is endemic throughout the tropics. Of the approximately billion people worldwide who are exposed annually billion are at high risk; the World Health Organization (WHO) states that more than million developed symptomatic malaria in [ ]. Between and , the number of reported annual malaria cases in malaria-eliminating countries decreased by percent from million to cases ]. Most of these are attributable to P. falciparum, but P. vivax and P. knowlesi can also cause severe disease. Malaria deaths peaked at million in and fell to million in ( children years and individuals years); over percent of the deaths occur in sub-Saharan Africa [ ]. The WHO’s estimates of deaths from malaria ( in uncertainty range to ) are approximately half the reliable estimates above. Malaria is transmitted via the bite of a female Anopheles spp mosquito, which occurs mainly between dusk and dawn. Other comparatively rare mechanisms for transmission include congenitally acquired disease, blood transfusion, sharing of contaminated needles, and organ transplantation . Malaria occurs throughout most of the tropical