Population dynamics with complex biological interactions, accounting for
uncertainty quantification, are 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.