William Obeng – Denteh, Emmanuel Appoh Andam, Lawrence Obiri – Apraku and Wallace Agyeil
In this work, we present and analyze amathematical epidemiological model for Vibrio cholerae (Cholera) with an incorporated control strategy. Cholera is regarded generally as a disease of the poor and it affects areas that lack access to safe drinking water and sense of hygiene. An epidemiological mathematical model for the transmission dynamics of cholera, with control strategies is formulated in this paper. The epidemiological model formulated is designed into compartments which lead to a system of differential equations for the transmission dynamics of cholera with a control strategy of water treatment being proposed. It was assumed in the model that cholera in contracted when an individual comes into contact and ingest contaminated water. The equilibrium points of the model are found and their stability is investigated. The results showed that the disease free equilibrium is locally asymptotically stable under suggested conditions on the parameters given in the model (i.e. cholera can be eradicated under such conditions in time bound). It was then concluded from the results that treatment of water is an effective method of controlling and eradicating cholera as well as public education on the disease. The numerical simulations and graphical solutions of the differential equations were carried out with Matlab application software.
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