Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations

In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of coupled stochastic differential equations. This limit process is complemented with socio-ecological and environmental factors. For the resulting system we establish well-posedness, positivity, and the non-attainability of extinction boundaries, together with its long-term behavior and numerical approximation, relying on ad-hoc arguments to handle the super-linear growth and non-Lipschitz coefficients. Finally, we illustrate some of our findings with numerical experiments.