Homogenization, sex, and differential motility predict spread of chronic wasting disease in mule deer in southern Utah

Chronic wasting disease (CWD) is an infectious prion disease that affects mule deer, along with other Cervids. It is a slow-developing, fatal disease which is rare in the free-ranging deer population of Utah. We present a sex-structured, spatial model for the spread of CWD over heterogeneous landscapes, incorporating both horizontal and environmental transmission pathways. To connect the local movement of deer to the regional spread of CWD, we use ecological diffusion with motility coefficients estimated from mule deer movement data. Ecological diffusion allows for aggregation of populations in desirable habitats and therefore allows for an interaction between density dependent disease transmission and landscape structure. The major innovation presented is use of homogenization to accelerate simulations of disease spread in southeastern Utah, from the La Sal Mountains near Moab to the Abajo Mountains near Monticello. The homogenized model provides accuracy while maintaining fidelity to small-scale habitat effects on deer distribution, including differential aggregation in land cover types with high residence times, with errors comparable to the order parameter measuring separation of small and large scales (ϵ≈.01\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon \approx .01$$\end{document} in this case). We use the averaged coefficients from the homogenized model to explore asymptotic invasion speed and the impact of current population size on disease spread in southeastern Utah.