Characterizing Infectious Disease Progression Through Discrete States Using Hidden Markov Models

Infectious disease management relies on accurate characterization of disease progression so that transmission can be prevented. Slowly progressing infectious diseases can be difficult to characterize because of a latency period between the time an individual is infected and when they show clinical signs of disease. The introduction of Mycobacterium avium ssp. paratuberculosis (MAP), the cause of Johne's disease, onto a dairy farm could be undetected by farmers for years before any animal shows clinical signs of disease. In this time period infected animals may shed thousands of colony forming units. Parameterizing trajectories through disease states from infection to clinical disease can help farmers to develop control programs based on targeting individual disease state, potentially reducing both transmission and production losses due to disease. We suspect that there are two distinct progression pathways; one where animals progress to a high-shedding disease state, and another where animals maintain a low-level of shedding without clinical disease. We fit continuous-time hidden Markov models to multi-year longitudinal fecal sampling data from three US dairy farms, and estimated model parameters using a modified Baum-Welch expectation maximization algorithm. Using posterior decoding, we observed two distinct shedding patterns: cows that had observations associated with a high-shedding disease state, and cows that did not. This model framework can be employed prospectively to determine which cows are likely to progress to clinical disease and may be applied to characterize disease progression of other slowly progressing infectious diseases.