A primer on the application of Markov chains to the study of wildlife disease dynamics

Abstract

1. For wildlife researchers, disease specialists and policy analysts unfamiliar with the mathematical/statistical language of disease models, translation of probability statements into meaningful terms for disease research and control may be challenging. Markov chain models are powerful tools, applicable to the study of disease dynamics that allow straightforward calculations of easily interpretable metrics of interest including probabilities of infection/recovery, expected times to initial infection, duration of illness and life expectancies for susceptible and infected individuals. 2. We present the basic principles and assumptions behind Markov chain modelling with an intuitive interpretation of parameter estimates and a step‐by‐step guide (including software code) for implementing this approach in the study of wildlife diseases. We also include an explanation of the estimation process necessary to implement Markov chain modelling (i.e. estimating the probability of state transitions between consecutive time steps) from typical survey data. 3. We demonstrate the usefulness and ease of calculation of Markov chains through an example using a house finch Carpodacus mexicanus – Mycoplasma gallisepticum (MG) system. Our results show how semi‐weekly transition estimates of susceptible and infected individuals can be used to estimate a wide array of seasonal disease‐associated metrics. 4. Markov chain modelling can provide a basic understanding of parameters estimated from wildlife disease studies, and can aid in understanding the implications of disease on wildlife populations and in evaluation of control measures. We envision this paper serving as an entry point into the extensive literature and potential applications of Markov chains in epidemiological modelling.