On reaction–diffusion equations derived from a PEPA model

This work presents an extension of the fluid approximation to the diffusion approximation for a PEPA model. The diffusion approximation leads to a reaction–diffusion system in which the spatial or location information is considered, while it is ignored in the fluid approximation approach. The fundamental results for the solution of the reaction–diffusion equations, such as the existence, uniqueness, positivity and convergence, have been established. Numerical simulations are also given to illustrate the analytical results.