Fundamental results on the reaction–diffusion equations associated with a PEPA model

This paper presents an extension of the fluid approximation of a PEPA model by augmenting with diffusion to take spatial information into account, which is described by a reaction–diffusion system with homogeneous Neumann boundary conditions. The existence and uniqueness of the solution are given, positivity and boundedness of the solution to the system are also established. Moreover, sufficient conditions for the convergence are discussed under different cases. Our results show that the action rates determine the behavior of positive solutions. Numerical simulations are presented to illustrate the analytical results.