An Epidemiological Model of Malaria at Techiman Municipality, Ghana

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.