A Spatial Model of Chronic Wasting Disease and the Optimal Placement of a Sight-Based Cull

Abstract Chronic wasting disease (CWD) is a fatal prion disease of cervids that spreads by direct contact and through a persistent environmental reservoir. We ask where and when a cull restricted to the clinically affected animals that field crews can identify should be placed on a real landscape, and what it can achieve. We formulate a five-compartment (susceptible, exposed, pre-clinical, clinical, environmental) reaction–diffusion model on a surface built from digital elevation data, with land cover setting the carrying capacity and slope and land cover setting an anisotropic diffusion tensor. We optimize a space- and time-dependent removal rate on the clinical class, computing gradients with the exact discrete adjoint of the finite element scheme. A closed-form bound gives the lowest control reproduction number such a cull can reach. With our parameters, pre-clinical animals generate 39.5% of local transmission, and maximal effort leaves it at or above 1.36 across our sweep. Simulations across reservoir persistence and transmissibility confirm that the optimal cull slows but never halts the invasion. The front retains 56–94% of its uncontrolled speed, and the control recovers 7–53% of the accumulated loss of susceptible deer. Where the herd is depleted, optimal effort forms a ring at the leading edge, 12–19 km ahead of the clinical peak. Cumulative incidence can rise under control even as per-capita risk falls, because the cull keeps more susceptible deer alive. On three Colorado landscapes, terrain and land cover barely change the benefit, and the cull needs 26–35% less effort, since less ground carries the invasion. Mathematics Subject Classification: 92D30; 49K20; 35K57; 65M60