Estimation of contact time among animals from telemetry data

Continuous processes in most applications are measured discretely with error. This complicates the task of detecting intersections and the number of intersections between two continuous processes (i.e., when the processes have the same value). Intersections of continuous processes are scientifically important but challenging to estimate from data. For example, in the field of animal ecology, intersections of the paths of moving animals tracked with satellite technologies can be used to understand disease transmission. We illustrate how to quantify contact between animals using telemetry data (i.e., the recorded locations of an animal over time). We introduce our method to quantify contact time with accessible concepts from introductory stochastic process literature, such as Brownian motion. Then, we provide two data examples using white-tailed deer (Odocoileus virginianus) and mule deer (Odocoileus hemionus) telemetry data in a region with high prevalence of chronic wasting disease. Our work provides a needed connection between existing model-based literature for animal movement and rule-based literature for animal interaction. Further, our work illustrates a unique statistical problem receiving minimal attention with broad applicability in human and livestock tracking.