Managing Chronic Wasting Disease with Direct and Environmental Transmission in Greater Yellowstone Area Elk: A Perturbation Approach to Dynamic Optimization with Multiple State Variables

Chronic Was,ng Disease (CWD) poses a major threat to Greater Yellowstone Area elk. CWD, which is always fatal, spreads through both direct contact and persistent environmental contamina,on via prions. Most bioeconomic studies on wildlife disease management focus on problems involving only direct transmission. Here we examine both direct and environmental transmission pathways. Analy,cally, we find environmental transmission makes disease control more difficult and costly, but not impossible. Numerically, we find environmental transmission drama,cally amplifies disease severity in the op,mal steady state, in spite of significantly greater controls being applied than if only direct transmission maJered. A second contribu,on is a new approach for numerically solving mul,-state, con,nuous-,me op,mal control models. Specifically, we use a combina,on of perturba,on methods (applied to highdimensional, stable invariant manifolds) and es,ma,on to obtain feedback control func,ons that can generate stable trajectories to the op,mal steady states from different ini,al states.