Scenario-aware control of multi-pathway spread processes: Application to biological invasions

Optimal control of spread processes over networks is a challenging problem, even for simple diffusion models. Real-world processes—such as infectious disease outbreaks and biological invasions—often involve multiple spread pathways and time-varying network dynamics. In this work, we address the problem of region-wide interventions, where the goal is to select an optimal set of regions (groups of nodes) in a network to minimize spread, subject to budget constraints, intervention delays, and a given spread scenario which reflects prior knowledge of the process — such as initial infection locations, parameter estimates, and other context-specific assumptions. We present a general approach based on integer linear programming and sample average approximation, applicable across a broad class of diffusion models. We also establish theoretical performance guarantees for our method within the bicriteria approximation framework. To demonstrate its effectiveness, we apply the approach to model the spread of a representative agricultural pest. Our method yields near-optimal solutions and consistently outperforms standard baselines. The results emphasize the value of scenario-specific intervention strategies, showing that early action can significantly reduce spread under limited budgets and produce stable outcomes even under model uncertainty.