A nonstandard finite difference method applied to a mathematical cholera model with spatial diffusion.

In this paper, we propose a nonstandard finite difference (NSFD) scheme to solve numerically a cholera epidemic model with spatial diffusion. Through constructing discrete Lyapunov functions, we prove the globally asymptotical stabilities of the diseasefree equilibrium and the chronic infection equilibrium, which coincide with the corresponding continuous model. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]