Mathematical Modeling and Multi-Period Resource Allocation for Invasive Plant Control

Effective control of invasive plant species involves allocating limited management resources across space and time in a manner consistent with underlying population dynamics and operational constraints. This study presents a discrete-time, spatially explicit mathematical model describing the expansion of Chinese privet (Ligustrum spp.), incorporating key biological processes such as seed dispersal, vegetative root propagation, and heterogeneous environmental suitability across a landscape grid. Model parameters governing growth and dispersal are calibrated using published ecological studies and field data compiled by collaborators. The ecological dynamics are coupled with a constrained multi-period optimization framework formulated as a mixed-integer linear programming (MILP) problem that determines when and where control actions should be implemented to minimize long-term reinfestation risk with finite budgets and treatment capacity. To address the multi-period decision structure, the optimization is implemented using a rolling-horizon solution approach, allowing sequential allocation decisions while updating the system state over time. The decision model explicitly accounts for treatment thresholds, spatial prioritization rules, and logistical limitations, enabling the evaluation of realistic management strategies over successive time steps. Simulation results demonstrate that temporally coordinated interventions and targeted spatial prioritization substantially reduce invasion intensity compared to uniform or short-term control policies. In particular, early intervention in high-connectivity cells yields disproportionate long-term benefits by suppressing secondary spread pathways. The proposed integrated modeling approach provides a quantitative decision-support tool for comparing alternative intervention scenarios, assessing trade-offs between cost and effectiveness, and identifying robust management policies under uncertainty. Overall, the framework supports evidence-based, cost-aware planning for invasive species control programs and can be adapted to other spatially spreading invasive organisms.