  Wildlife disease surveillance programs and research studies track infection
and identify risk factors for wild populations, humans, and agriculture. Often,
several types of samples are collected from individuals to provide more
complete information about an animal's infection history. Methods that jointly
analyze multiple data streams to study disease emergence and drivers of
infection via epidemiological process models remain underdeveloped.
Joint-analysis methods can more thoroughly analyze all available data, more
precisely quantifying epidemic processes, outbreak status, and risks. We
contribute a paired data modeling approach that analyzes multiple samples from
individuals. We use "characterization maps" to link paired data to
epidemiological processes through a hierarchical statistical observation model.
Our approach can provide both Bayesian and frequentist estimates of
epidemiological parameters and state. We motivate our approach through the need
to use paired pathogen and antibody detection tests to estimate parameters and
infection trajectories for the widely applicable susceptible, infectious,
recovered (SIR) model. We contribute general formulas to link characterization
maps to arbitrary process models and datasets and an extended SIR model that
better accommodates paired data. We find via simulation that paired data can
more efficiently estimate SIR parameters than unpaired data, requiring samples
from 5-10 times fewer individuals. We then study SARS-CoV-2 in wild
White-tailed deer (Odocoileus virginianus) from three counties in the United
States. Estimates for average infectious times corroborate captive animal
studies. Our methods use general statistical theory to let applications extend
beyond the SIR model we consider, and to more complicated examples of paired
data.
