Homogenization Reveals Large-Scale Dynamics in the Spread of Chronic Wasting Disease.

Abstract

Thresholds in environmental transmission can significantly alter the dynamics of disease spread in wildlife. However, the impact of thresholds in landscapes with high spatial variability is not well understood. We investigate this phenomenon in chronic wasting disease (CWD), a degenerative cervid illness exhibiting direct transmission between individuals and indirect transmission through environmental hazard. The indirect pathway exhibits threshold behavior analogous to a strong Allee effect. We derive a partial differential equation (PDE) model for CWD on the scale of hours and tens of meters. Leveraging highly variable landscape structure, we homogenize this model to yield an asymptotically accurate approximal model on the scale of years and kilometers. Our homogenized model describes the aggregate effect of thresholded transmission on large scales - to our knowledge, the first time such a description has been identified. The model predicts that direct transmission in CWD will lead to pulled fronts, whereas indirect transmission generates pushed fronts. Pushed fronts allow CWD to spread even when infectives infect less than one susceptible on average. We use a hypothetical binary distribution of habitat types to showcase the homogenized model's ability to predict how distribution of cover in a landscape can influence CWD spread and potential mitigation efforts.