Global dynamics of reaction–diffusion systems with delays Original Research Article

Taking the effect of spatial diffusion into account, we introduce an exponential ordering and give sufficient conditions under which reaction–diffusion systems with delays generate monotone semi-flows on a suitable phase space even if they are not quasi-monotone. The powerful theory of monotone semi-flows is applied to describe the threshold dynamics for a nonlocal delayed reaction–diffusion system modelling the spread of bacterial infections.