Learning complex spatial dynamics of wildlife diseases with machine learning-guided partial differential equations

Abstract Emerging wildlife pathogens often display geographic variability due to landscape heterogeneity. Modeling approaches capable of learning complex, non-linear spatial dynamics of diseases are needed to rigorously assess and mitigate the effects of pathogens on wildlife health and biodiversity. We propose a novel machine learning (ML)-guided approach that leverages prior physical knowledge of ecological systems, using partial differential equations. We present our approach, taking advantage of the universal function approximation property of neural networks for flexible representation of the underlying dynamics of the geographic spread and growth of wildlife diseases. We demonstrate the benefits of our approach by comparing its forecasting power with commonly used methods and highlighting the obtained insights on disease dynamics. Additionally, we show the theoretical guarantees for the approximation error of our model. We illustrate the implementation of our ML-guided approach using data from white-nose syndrome (WNS) outbreaks in bat populations across the US. WNS is an infectious fungal disease responsible for significant declines in bat populations. Our results on WNS are useful for disease surveillance and bat conservation efforts. Our methods can be broadly used to assess the effects of environmental and anthropogenic drivers impacting wildlife health and biodiversity.