Varroa mites are a major global threat to honeybee colonies. Combining digital twins with scenario-generating models can be an enabler of precision apiculture, allowing for monitoring Varroa spread, generating treatment scenarios under varying conditions, and running remote interventions. This paper presents the conceptual design of this system for large-scale Varroa management in honeybee apiaries, with initial validation conducted through simulations and feasibility analysis. The design followed a design research framework. The proposed system integrates a wireless sensor network for continuous hive sensing, image capture, and remote actuation of treatment. It employs generative time-series models to forecast colony dynamics and a statistical network model to represent inter-colony spread; together, they support spread scenario prediction and what-if evaluations of treatments. The system evolves through continuous updates from field data, improving the accuracy of spread and treatment models over time. As part of our design research, an early feasibility assessment was carried out through the generation of synthetic data for spread model pretraining. In addition, a node-level energy budget for sensing, communication, and in-hive treatment was developed and matched with battery capacity and life calculations. Overall, this work outlines a path toward real-time, data-driven Varroa management across apiary networks, from regional to cross-border scales.