Dynamic-Bayesian disease management under state uncertainty: learning and bovine tuberculosis control in New Zealand cattle

Abstract

In the context of bovine tuberculosis (bTB) control in New Zealand cattle, we address the problem of management under uncertain disease prevalence by integrating a model of disease transmission and Bayesian learning from testing. We show the implications of accounting for the full dynamic value of information for setting levels of investment in, and targeting of, disease control measures. In the process, we provide a methodology to addressing problems in which learning occurs regarding an uncertain and endogenous state variable. bTB is an infectious and potentially fatal disease of both animals and humans that persists throughout much of the world. In addition to health impacts, trade may be restricted by potential importers that are averse to the possibility of direct transmission via live cattle movements and via animal products to consumers. Despite intensive and sustained control efforts in New Zealand, eradication has been encumbered by characteristics of the pathogen and environmental and anthropogenic factors: a long incubation period, a pervasive but elusive wild host (the common brushtail possum), imperfect testing methods, and the diffuse nature of production. These features have allowed bTB to remain endemic among New Zealand cattle and deer herds since the mid-to-late 20th century, and substantially increased the difficulty of determining prevalence. For an endemic disease such as this, there may be an especially high value to the central veterinary authority in understanding the prevalence of the disease, particularly at a regional scale. More specifically, test results may be used to better inform future testing choices. Modifications of existing bioeconomic models are necessary to capture the value of additional information regarding prevalence. Implicit in existing bioeconomic models of bTB control is the unrealistic assumption that the central veterinary authority knows perfectly the number of facilities that are latently infected without knowing specifically which facilities are infected. We address uncertainty over the true state of disease prevalence by specifying a belief distribution. We then obtain results by using Bayesian and dynamic programming methods to optimize a dynamical system of disease spread and control in which the central authority’s beliefs regarding prevalence is modeled as a partially observed Markov decision processes. The belief distribution is characterized by two parameters that replace the true but uncertain state variable in the dynamic programming problem. The dynamics are complicated by the fact that decision makers are learning about a moving target: an evolving and endogenous disease prevalence. In each period, the central veterinary authority must update its beliefs using the information gained from testing, and using its understanding of the changes in prevalence that result from infections and recoveries. These physical processes are determined in part by the number of facilities that receive testing and subsequent targeted treatment, making prevalence endogenous. This extension allows us to examine efficient testing and application of targeted controls while explicitly modeling uncertainty and learning about the unobserved state. Our model captures both the gains from targeting animal movement restrictions and culling efforts and from using additional information to inform future testing decisions.