The global output of academic publications exceeds 5 million articles per year, making it difficult for humans to keep up with even a tiny fraction of scientific output. We need methods to navigate and interpret the artifacts -- texts, graphs, charts, code, models, and datasets -- that make up the literature. This paper evaluates various methods for extracting mathematical model variables from epidemiological studies, such as ``infection rate ($α$),'' ``recovery rate ($γ$),'' and ``mortality rate ($μ$).'' Variable extraction appears to be a basic task, but plays a pivotal role in recovering models from scientific literature. Once extracted, we can use these variables for automatic mathematical modeling, simulation, and replication of published results. We introduce a benchmark dataset comprising manually-annotated variable descriptions and variable values extracted from scientific papers. Based on this dataset, we present several baseline methods for variable extraction based on Large Language Models (LLMs) and rule-based information extraction systems. Our analysis shows that LLM-based solutions perform the best. Despite the incremental benefits of combining rule-based extraction outputs with LLMs, the leap in performance attributed to the transfer-learning and instruction-tuning capabilities of LLMs themselves is far more significant. This investigation demonstrates the potential of LLMs to enhance automatic comprehension of scientific artifacts and for automatic model recovery and simulation.