The fitting of general force-of-infection models to wildlife disease prevalence data

Researchers and wildlife managers increasingly find themselves in situations where they must deal with infectious wildlife diseases such as chronic wasting disease, brucellosis, tuberculosis, and West Nile virus. Managers are often charged with designing and implementing control strategies, and researchers often seek to determine factors that influence and control the disease process. All of these activities require the ability to measure some indication of a disease's foothold in a population and evaluate factors affecting that foothold. The most common type of data available to managers and researchers is apparent prevalence data. Apparent disease prevalence, the proportion of animals in a sample that are positive for the disease, might seem like a natural measure of disease's foothold, but several properties, in particular, its dependency on age structure and the biasing effects of disease-associated mortality, make it less than ideal. In quantitative epidemiology, the "force of infection," or infection hazard, is generally the preferred parameter for measuring a disease's foothold, and it can be viewed as the most appropriate way to "adjust" apparent prevalence for age structure. The typical ecology curriculum includes little exposure to quantitative epidemiological concepts such as cumulative incidence, apparent prevalence, and the force of infection. The goal of this paper is to present these basic epidemiological concepts and resulting models in an ecological context and to illustrate how they can be applied to understand and address basic epidemiological questions. We demonstrate a practical approach to solving the heretofore intractable problem of fitting general force-of-infection models to wildlife prevalence data using a generalized regression approach. We apply the procedures to Mycobacterium bovis (bovine tuberculosis) prevalence in bison (Bison bison) in Wood Buffalo National Park, Canada, and demonstrate strong age dependency in the force of infection as well as an increased mortality hazard in positive animals.