Cereal grains, oilseeds, and pulses (collectively referred to as grains) form a major portion of daily intake for humans and domesticated animals and hold greater economic value for producers and grain industry. Often grain losses (qualitative and quantitative) occur due to improper management of grains during storage. Grain storage comprises of several interactions among biotic and abiotic factors that makes understanding of ecosystem quite complex. Over the years, mathematical modeling has emerged as a powerful tool for assessment, prediction, and simulation of real-time storage conditions. This manuscript presents a comprehensive review on various modeling approaches that are used for solving grain storage problems. Different solution techniques of mathematical formulations using analytical and numerical approaches (finite element, finite difference, finite volume, and discrete element modeling) are explained. The testing and validation are critical steps and must be considered during model development process. Reports are available for the prediction of temperature, moisture, and gas diffusion profiles in grain bins for different storage conditions. Similarly, works have been attempted for determination of spatial temporal distribution of stored products insect in grain bulks as well as models to predict development of fungi in grains have been reported. However, a comprehensive grain storage model through coupling of physical models (thermal, moisture, and gas diffusion) with biological models (population dynamics and dispersal) as well as economic models is needed. The advancements in information technology would aid in analyzing the available data from laboratory and field studies for forming an online database. Appropriate global cooperation and coordination of available data could help in accessing information about stored grains and level of infestation or infection at any given time. Early prediction of storage conditions in grain bins are possible through mathematical modeling approach that should help in establishing better grain management protocols.

中文翻译：

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储粮生态系统管理的数学模型：方法、机遇和研究需求

谷物、油籽和豆类（统称为谷物）构成了人类和家养动物日常摄入量的主要部分，对生产者和粮食工业具有更大的经济价值。由于谷物在储存过程中管理不当，经常会发生谷物损失（质量和数量）。粮食储存由生物和非生物因素之间的多种相互作用组成，这使得对生态系统的理解变得相当复杂。多年来，数学建模已成为评估、预测和模拟实时存储条件的强大工具。本手稿对用于解决粮食储存问题的各种建模方法进行了全面回顾。解释了使用分析和数值方法（有限元、有限差分、有限体积和离散元建模）的数学公式的不同求解技术。测试和验证是关键步骤，在模型开发过程中必须考虑。可提供报告来预测不同储存条件下粮仓中的温度、湿度和气体扩散曲线。同样，已经尝试确定谷物中储存产品昆虫的时空分布，并报告了预测谷物中真菌发育的模型。然而，需要通过物理模型（热、水分和气体扩散）与生物模型（种群动态和扩散）以及经济模型的耦合来建立全面的粮食储存模型。信息技术的进步将有助于分析实验室和现场研究的可用数据，以形成在线数据库。适当的全球合作和现有数据的协调有助于获取有关储存谷物以及任何特定时间的侵染或感染水平的信息。通过数学建模方法可以早期预测粮仓的储存条件，这有助于建立更好的粮食管理协议。