A Study of a Metapopulation Model Using the Stochastic Reaction Diffusion Master Equation

Many biological systems involve both the noise in chemical reaction process and diffusion in space between the molecules involved in the reactions. Since the copy numbers of participating species often are small, their stochastic behavior comes into play. The reaction-diffusion master equation (RDME) is a stochastic modeling of the reaction-diffusion process. In RDME, the space is partitioned into compartments and a well mixing of species is considered inside each compartment. Contrary to the chemical master equation (CME) that does not analyze the diffusion of the molecules between the components, the RDME is more complex and has a substantially larger state space than the CME. In this study we tackle a metapopulation model using the RDME formulation. Numerical methods are used to analyze and predict the behavior of the model.