Dynamically consistent discrete metapopulation model

Abstract

In this paper we construct nonstandard difference schemes, which are dynamically consistent with a metapopulation model formulated by Keymer et al. in 2000, i.e. preserve all dynamical properties of the differential equations of the model. These properties are: monotone convergence, boundedness, local asymptotic stability and especially, global stability of equilibria and non-periodicity of solutions. Numerical examples confirm the obtained theoretical results of the properties of the constructed difference schemes.