Managing fungal diseases with optimal control methods and individual-based models

Background/Question/Methods

Optimal control techniques can be used to derive cost-effective management strategies for wildlife disease, but require appropriate models for disease dynamics. Many fungal diseases exhibit common properties that affect these dynamics: hosts can be repeatedly infected, effects of disease are load-dependent, and disease can originate from persistent reservoirs in the environment or other, unaffected hosts. Fungal diseases can suppress host populations and lead to extinction, and management goals may include host conservation and disease eradication. This combination of factors favors stochastic, individual-based models (IBMs), which can simulate individual variation in disease loads and extinction behavior.

Applying optimal control to IBMs is challenging due to IBMs' high dimensionality, which precludes robust exploration of state space. "Multi-scale" or "equation-free" (EF) techniques can be used to reduce IBM states to a small number of variables. Here, I demonstrate use of EF methods in optimal control, applied to the problem of fungal disease management for conservation.

Results/Conclusions

I examine a management problem using a model based on sudden oak death dynamics. In the model, hosts provide an ecosystem service and disease control can be exerted, with cost, by eliminating environmental spore loads or culling hosts.

EF techniques calculate artificial derivatives by simulating stochastic IBMs in short, repeated bursts, and averaging outcomes. These artificial derivatives are then used to estimate changes at the population scale. I use these derivatives to solve the management problem using Hamiltonian-style optimal control. I show how relative cost and population size modify the effectiveness of eliminating reservoirs of disease and culling diseased hosts.

Slides and related materials will be archived at http://dx.doi.org/10.6084/m9.figshare.1312935 prior to the session.