Spatiotemporal Modeling and Analysis of Disease Spread in Wildlife

Abstract

Wildlife and wildlife diseases have been frequent topics in mathematical epidemiology. However, due to the complexity of real-world systems and the varying degree of randomness in the behavior of any one individual organism, it can be difficult to obtain reliable and accurate spatiotemporal results with any given methodology. In this work, we look at hemorrhagic diseases (HD) in white-tailed deer as a case study to explore statistical and mathematical modeling techniques for analyzing disease spread in wildlife. We concentrate on two modeling approaches to evaluate their capabilities and usefulness in predicting and analyzing the dynamics of wildlife diseases. Statistical modeling implemented with SaTScan enables us to identify significant clusters of disease activity, clusters that are significant with respect to geography or time or both. The spatial clusters of years 1980, 1988, 2007, 2012, and 2013 suggest patterns of outbreaks every six to eight years, with the next potential outbreak during 2018 - 2020. Using mathematical modeling with ordinary differential equations (ODE), we derive a model for the dynamics of the disease that includes the migration of the host. We also derive the basic reproduction number R₀ of this model to uncover the conditions that lead to an outbreak of the disease. In addition, we also apply several techniques using MATLAB to estimate the parameters of such a set of ODE which are useful when the available data set is limited in size.