Ongoing surveillance protects tanoak whilst conserving biodiversity: applying optimal control theory to a spatial simulation model of sudden oak death

Abstract

The sudden oak death epidemic in California is spreading uncontrollably. Large-scale eradication has been impossible for some time. However, small-scale disease management could still slow disease spread. Although empirical evidence suggests localised control could potentially be successful, mathematical models have said little about such management. By approximating a detailed, spatially-explicit simulation model of sudden oak death with a simpler, mathematically-tractable model, we demonstrate how optimal control theory can be used to unambiguously characterise effective time-dependent disease management strategies. We focus on protection of tanoak, a tree species which is culturally and ecologically important, but also highly susceptible to sudden oak death. We identify management strategies to protect tanoak in a newly-invaded forest stand, whilst also conserving biodiversity. We find that thinning of bay laurel is essential early in the epidemic. We apply model predictive control, a feedback strategy in which both the approximating model and the control are repeatedly updated as the epidemic progresses. Adapting optimal control strategies in this way is vital for effective disease management. This feedback strategy is robust to parameter uncertainty, limiting loss of tanoak in the worst-case scenarios. However, the methodology requires ongoing surveillance to re-optimise the approximating model. This introduces an optimal level of surveillance to balance the high costs of intensive surveys against improved management resulting from better estimates of disease progress. Our study shows how detailed simulation models can be coupled with optimal control theory and model predictive control to find effective control strategies for sudden oak death. We demonstrate that control strategies for sudden oak death must depend on local management goals, and that success relies on adaptive strategies that are updated via ongoing disease surveillance. The broad framework allowing the use of optimal control theory on complex simulation models is applicable to a wide range of systems.