Abstract: By applying a nonstandard finite difference scheme, we construct and solve a discretized cholera epidemic model. The scheme can ensure that equilibrium points, the positivity and boundedness of solutions to the discrete model is the same as the original mathematical model. We have proved that when the basic reproduction number is less than 1, the disease-free equilibrium is locally and globally asymptotically stable. When the basic reproduction number is greater than 1, we prove that the endemic equilibrium is globally asymptotically stable by constructing a suitable Lyapunov function. Finally, the NSFD scheme can be well suited to numerically solve the cholera outbreak in Zimbabwe.

Key words: Cholera, nonstandard finite difference, stability, Lyapunov function