Demonstrating true disease freedom distinct from low prevalence across time: A zero inflated model with disease introduction and spread considerations

International standards guide claims of disease freedom status, supported by surveillance-based evidence of disease absence through time. Conventional methods for assessing absence have trouble distinguishing between low (below a detection threshold) and zero prevalence of disease. Current methods addressing this limitation lack the ability to incorporate historical data and propagate evidence of absence through time when there is potential for disease introduction. Further, maintenance across time requires continuous assurance which is supported by incorporating historical data and disease dynamics. Our new model framework, Zero-Inflated Prevalence for FREEdom over Time (ZIP-FREE-T), is a Bayesian model that (1) includes zero-inflated beta prevalence distributions affording probability computation at any threshold prevalence whether zero (absolute absence) or non-zero (effective absence), (2) infers the effect of a previously missed infection using spread dynamics, and (3) incorporates introduction risk addressing both the probability and magnitude of an introduction event. We apply our model to evaluate sample sizes needed to maintain assurance of disease freedom from Perkinsus marinus in a hypothetical population of the oyster Crassostrea virginica. Sensitivity analysis for this example suggests specified prior distributions and spread rates are non-ignorable. Solutions offered by ZIP-FREE-T bring awareness to, and allow discussion and planning around, issues central to population health management. These include the probability of zero rather than low prevalence, the potential for disease introduction and subsequent spread, as well as the effect of risk mitigation on the assurance of disease freedom.