Asymptotic behaviour of reaction-diffusion systems in population and epidemic models. The role of cross diffusion.

Cross diffusion has been widely considered in the mathematical modelling of spatially structured ecological and epidemic systems, either in the mechanical description of diffusion or in the stochastic point process description of interacting populations. In this paper mathematical results recently obtained by the authors about the asymptotic behaviour of reaction-diffusion systems with full matrices of diffusion are applied to classes of biological systems.