A Discrete-Time Zero-inflated Beta Bayesian Model for Disease Prevalence Over Time

Current methods for estimating disease freedom probabilities in aquaculture combine prior disease freedom probability with data likelihood and introduction probability to produce posterior freedom over time. These methods aim to establish freedom from disease above a design prevalence. In this study, we present updates to this methodology that differentiate between absolute freedom (actual zero prevalence) and effective freedom (disease occurring below the design prevalence). We implement these updates using a zero-inflated Beta distribution for both prior prevalence and introduction prevalence at each time step. Additionally, we introduce an assumption of exponential disease progression over time to allow for natural increases. We derive the posterior distribution and validate our methodology through simulation. Our approach offers a more nuanced assessment of disease freedom, enhancing decision-making for aquaculture health management.

Clark Kogan
Clark Kogan
Washington State University