Disease dynamics in wild populations: modeling and estimation: a review

Models of infectious disease dynamics focus on describing the temporal and spatial variations in disease prevalence, and on understanding the factors that affect how many cases will occur in each time period and which individuals are likely to become infected. Classical methods for selecting and fitting models, mostly motivated by human diseases, are almost always based solely on raw counts of infected and uninfected individuals. We begin by reviewing the main classical approaches to parameter estimation, and some of their applications. We then review recently developed methods which enable representation of component processes such as infection and recovery, with observation models that acknowledge the complexities of the sampling and detection processes. We demonstrate the need to account for detectability in modeling disease dynamics, and explore a number of mark-recapture and occupancy study designs for estimating disease parameters while simultaneously accounting for variation in detectability. We highlight the utility of different modeling approaches and also consider the typically strong assumptions that may actually serve to limit their utility in general application to the study of disease dynamics (e.g., assignment of individuals to discrete disease states when underlying state space is more generally continuous; transitions assumed to be simple first-order Markov; temporal separation of hazard and transition events).