Invasive alien species pose major ecological and socio-economic challenges, especially when they exert strong predation pressure on native resources while offering opportunities for commercial use. Addressing this dual role requires models that integrate ecological dynamics, economic incentives, and institutional policies. This paper develops a general bioeconomic framework for a predator–prey system subject to human interventions. The native resource is harvested for economic purposes, while the invasive predator can be controlled through both commercial exploitation and institutional removal. The analysis combines equilibrium methods and optimal control over finite horizons, capturing the interaction between long-run ecological regimes and short-term management objectives. The results characterize threshold conditions for species coexistence and identify how harvesting and institutional removal affect the ecological regimes of the system. The analysis shows that moderate exploitation of the invasive predator can enlarge the coexistence region, whereas eradication requires removal efforts exceeding its intrinsic growth rate. The optimal control analysis highlights the role of coordinated management instruments, with numerical results indicating that mixed market and institutional strategies outperform single-instrument policies. The framework is inspired by the interaction between the invasive blue crab (Callinectes sapidus) and native bivalves in Mediterranean coastal systems, and points to policy strategies that integrate ecological conservation, economic valorization, and institutional containment.

Controlling and planning the removal of invasive species are topics of outmost importance in management of natural resources because of the severe ecological damages and economic losses caused by non-native alien species. Optimal management strategies often rely on coupling population dynamics models with optimization procedures to achieve an effective allocation of limited resources for removing invasive species from hosting ecosystems. We analyse a parabolic optimal control model to simulate the best spatiotemporal strategy for the removal of the species when a budget constraint is applied. The model also predicts the species spread under the control action. We improve the capability of the model to reproduce realistic scenarios by introducing an advection term in the state equation. That allows to model the action of external forces, like currents or winds, which might bias dispersal in certain directions. The analytical properties of the model are discussed under suitable boundary conditions. As a further original contribution, we introduce a novel numerical procedure for approximating the solution reducing the computational costs in view of its implementation as a support decision tool. Then we test the approach by simulating the spread and the control of a hypothetical invasive plant in the territory of the Italian Sardinia island. To reproduce the anisotropy of the diffusion we include the effect of the altitude in the habitat suitability of the species.