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This study compares pandemic experiences of Missouri’s 115 counties based on rurality and sociodemographic characteristics during the 1918–20 influenza and 2020–21 COVID-19 pandemics. The state’s counties and overall population distribution have remained relatively stable over the last century, which enables identification of long-lasting pandemic attributes. Sociodemographic data available at the county level for both time periods were taken from U.S. census data and used to create clusters of similar counties. Counties were also grouped by rural status (RSU), including fully (100%) rural, semirural (1–49% living in urban areas), and urban (>50% of the population living in urban areas). Deaths from 1918 through 1920 were collated from the Missouri Digital Heritage database and COVID-19 cases and deaths were downloaded from the Missouri COVID-19 dashboard. Results from sociodemographic analyses indicate that, during both time periods, average farm value, proportion White, and literacy were the most important determinants of sociodemographic clusters. Furthermore, the Urban/Central and Southeastern regions experienced higher mortality during both pandemics than did the North and South. Analyses comparing county groups by rurality indicated that throughout the 1918–20 influenza pandemic, urban counties had the highest and rural had the lowest mortality rates. Early in the 2020–21 COVID-19 pandemic, urban counties saw the most extensive epidemic spread and highest mortality, but as the epidemic progressed, cumulative mortality became highest in semirural counties. Additional results highlight the greater effects both pandemics had on county groups with lower rates of education and a lower proportion of Whites in the population. This was especially true for the far southeastern counties of Missouri (“the Bootheel”) during the COVID-19 pandemic. These results indicate that rural-urban and socioeconomic differences in health outcomes are long-standing problems that continue to be of significant importance, even though the overall quality of health care is substantially better in the 21 st century. 

Summary Many real‐world scientific processes are governed by complex non‐linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non‐linear dynamic systems using data‐driven approaches. In this paper, we review the current literature on data‐driven discovery for dynamic systems. We provide a categorisation to the different approaches for data‐driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data‐driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work. 

Historically, two primary criticisms statisticians have of machine learning and deep neural models is their lack of uncertainty quantification and the inability to do inference (i.e., to explain what inputs are important). Explainable AI has developed in the last few years as a sub‐discipline of computer science and machine learning to mitigate these concerns (as well as concerns of fairness and transparency in deep modeling). In this article, our focus is on explaining which inputs are important in models for predicting environmental data. In particular, we focus on three general methods for explainability that are model agnostic and thus applicable across a breadth of models without internal explainability: “feature shuffling”, “interpretable local surrogates”, and “occlusion analysis”. We describe particular implementations of each of these and illustrate their use with a variety of models, all applied to the problem of long‐lead forecasting monthly soil moisture in the North American corn belt given sea surface temperature anomalies in the Pacific Ocean. 

Recent developments in the use of artificial intelligence in the diagnosis and monitoring of glaucoma are discussed. To set the context and fix terminology, a brief historic overview of artificial intelligence is provided, along with some fundamentals of statistical modeling. Next, recent applications of artificial intelligence techniques in glaucoma diagnosis and the monitoring of glaucoma progression are reviewed, including the classification of visual field images and the detection of glaucomatous change in retinal nerve fiber layer thickness. Current challenges in the direct application of artificial intelligence to further our understating of this disease are also outlined. The article also discusses how the combined use of mathematical modeling and artificial intelligence may help to address these challenges, along with stronger communication between data scientists and clinicians.