Modeling seasonal behavior changes and disease transmission with application to chronic wasting disease

Abstract

Behavior and habitat of wildlife animals change seasonally according to environmental conditions. Mathematical models need to represent this seasonality to be able to make realistic predictions about the future of a population and the effectiveness of human interventions. Managing and modeling disease in wild animal populations requires particular care in that disease transmission dynamics is a critical consideration in the etiology of both human and animal diseases, with different transmission paradigms requiring different disease risk management strategies. Since transmission of infectious diseases among wildlife depends strongly on social behavior, mechanisms of disease transmission could also change seasonally. A specific consideration in this regard confronted by modellers is whether the contact rate between individuals is density-dependent or frequency-dependent. We argue that seasonal behavior changes could lead to a seasonal shift between density and frequency dependence. This hypothesis is explored in the case of chronic wasting disease (CWD), a fatal disease that affects deer, elk and moose in many areas of North America. Specifically, we introduce a strategic CWD risk model based on direct disease transmission that accounts for the seasonal change in the transmission dynamics and habitats occupied, guided by information derived from cervid ecology. The model is composed of summer and winter susceptible-infected (SI) equations, with frequency-dependent and density-dependent transmission dynamics, respectively. The model includes impulsive birth events with density-dependent birth rate. We determine the basic reproduction number as a weighted average of two seasonal reproduction numbers. We parameterize the model from data derived from the scientific literature on CWD and deer ecology, and conduct global and local sensitivity analyses of the basic reproduction number. We explore the effectiveness of different culling strategies for the management of CWD: although summer culling seems to be an effective disease eradication strategy, the total culling rate is limited by the requirement to preserve the herd.