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We present a second-order high-resolution finite difference scheme to approximate the solution of a mathematical model of the transmission dynamics of Mycobacterium marinum (Mm) in an aquatic environment. This work extends the numerical theory and continues the preliminary studies on the model first developed in Ackleh et al. We also demonstrated that the model can be a tool to understand surprising or nonintuitive phenomena regarding competitive advantage in the context of biologically realistic growth, birth and death rates.