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The dynamics of ecological as well as chemical systems may depend onheterogeneous configurations. Heterogeneity in reaction-diffusion systems oftenincrease modelling and simulating difficulties when non-linear effects arepresent. One synthetic epidemic system with short range heterogeneouscomposition is modelled and its space-time evolution studied using maximumheterogeneity details. Two other modelling alternatives are applied, one ofthem using elementary mean-field variables, one other using non-localizedgeometrical parameters, so avoiding the limitations of the used mean-fieldmodel, while keeping significant features of more detailed models. Both thedetailed and the mean-field models are solved by means of the standard finitevolume method. The model with less defined geometry is solved by means of onemodified version of the finite volume method. Simulation results of the threemodels are compared. At the high diffusion range all models behave similarly.At moderate diffusion fluxes, the numerical results of the model with reducedgeometric details are in excellent agreement with the results of the detailedmodel. The simple mean-field model presents limited accuracy at low andmoderate values of the diffusion coefficient.

Model for heterogeneous reaction-diffusion systems with application to one epidemic