  In this paper nonstandard finite difference (NSFD) schemes of two
metapopulation models are constructed. The stability properties of the discrete
models are investigated by the use of a generalization of Lyapunov stability
theorem. Due to this result we have proved that the NSFD schemes preserve all
properties of the metapopulation models. Numerical examples confirm the
obtained theoretical results of the properties of the constructed difference
schemes. The method of Lyapunov functions proves to be much simpler than the
standard method for studying stability of the discrete metapopulation model in
our very recent paper.
