The growing complexity of decision-making in public health and health care has motivated an increasing use of mathematical modeling. An important line of health modeling is based on stock & flow diagrams. Such modeling elevates transparency across the interdisciplinary teams responsible for most impactful models, but existing tools suffer from a number of shortcomings when used at scale. Recent research has sought to address such limitations by establishing a categorical foundation for stock & flow modeling, including the capacity to compose a pair of models through identification of common stocks and sum variables. This work supplements such efforts by contributing two new forms of composition for stock & flow diagrams. We first describe a hierarchical means of diagram composition, in which a single existing stock is replaced by a diagram featuring compatible flow structure. Our composition method offers extra flexibility by allowing a single flow in the stock being replaced to split into several flows totalling to the same overall flow rate. Secondly, to address the common need of docking a stock & flow diagram with another "upstream" diagram depicting antecedent factors, we contribute a composition approach that allows a flow out of an upstream stock in one diagram to be connected to a downstream stock in another diagram. Both of these approaches are enabled by performing colimit decomposition of stock & flow diagrams into single-stock corollas and unit flows.

翻译：公共卫生与医疗决策日益增长的复杂性推动了数学模型的广泛应用。基于存量-流量图（stock & flow diagrams）的建模是健康建模的重要方向。此类建模提升了跨学科团队（负责最具影响力的模型）的透明度，但现有工具在规模化应用时存在若干缺陷。近期研究试图通过建立存量-流量建模的范畴论基础（包括通过识别共同存量和求和变量实现模型组合）来弥补这些不足。本研究提出两种新型存量-流量图组合方法以完善现有成果。首先描述一种层级式图组合方法，其中单个现有存量被替换为具有兼容流量结构的子图。该方法允许被替换存量中的单一流量分裂为多个流量（其总流量率保持不变），从而提供额外灵活性。其次，为解决存量-流量图与描述前置因素的"上游"图对接这一常见需求，我们提出一种组合方法：允许一个图中上游存量流出的流量与另一图中下游存量相连接。上述两种方法均通过将存量-流量图分解为单存量花冠（single-stock corollas）与单位流量（unit flows）的余极限（colimit）分解来实现。