  Population dynamics with complex biological interactions, accounting for
uncertainty quantification, is critical for many application areas. However,
due to the complexity of biological systems, the mathematical formulation of
the corresponding problems faces the challenge that the corresponding
stochastic processes should, in most cases, be considered in bounded domains.
We propose a model based on a coupled system of reflecting Skorokhod-type
stochastic differential equations with jump-like exit from a boundary. The
setting describes the population dynamics of active and passive populations. As
main working techniques, we use compactness methods and Skorokhod's
representation of solutions to SDEs posed in bounded domains to prove the
well-posedness of the system. This functional setting is a new point of view in
the field of modelling and simulation of population dynamics. We provide the
details of the model, as well as representative numerical examples, and discuss
the applications of a Wilson-Cowan-type system, modelling the dynamics of two
interacting populations of excitatory and inhibitory neurons. Furthermore, the
presence of random input current, reflecting factors together with Poisson
jumps, increases firing activity in neuronal systems.
