LEAPS-MPS: Exploring Properties of Linear Compartmental Models

This project explores how mathematical diagrams called linear compartmental models (LCMs) can help researchers understand the structure and behavior of systems involving movement or flow, including how diseases spread, how nutrients cycle through ecosystems, or how medications are processed in the body. These models represent systems as interconnected compartments, with arrows indicating how quantities move between them. The investigator aims to identify when meaningful information about these systems, such as flow rates, can be reliably extracted from data, and when different models might appear identical in practice. The project’s goal is to create simple, visual tests for analyzing these characteristics of LCMs, making the process more accessible and less computationally intensive. This project provides undergraduates with opportunities to participate in cutting-edge mathematical research and equips them with background needed to pursue further education. A new colloquium series will further expand students’ exposure to graduate-level research and support their preparation for advanced study.

This project addresses fundamental questions of identifiability and indistinguishability in linear compartmental models, which are widely used to represent dynamical systems with flow. Identifiability, the ability to recover model parameters from input-output data, has been well-studied for single-input, single-output, strongly connected LCMs, and this project extends the scope of current theory. The first research objective is to investigate irreducibility in LCMs, laying the groundwork for identifiability results for models with multiple inputs/outputs and weaker graph structures. A second objective focuses on a class of models known as skeletal path models, which are not strongly connected but have a well-understood structure and serve as promising candidates for generalizing identifiability theory. The final objective is to examine indistinguishability, a property in which structurally distinct models produce indistinguishable output behavior. The investigator and undergraduate collaborators will explore this question through the study of cycle models, which have been previously analyzed for identifiability but not for indistinguishability. The project emphasizes visual and combinatorial approaches to model analysis, enhancing accessibility for undergraduate researchers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Award Number: 2532620
Principal Investigator: Cashous Bortner
Funds Obligated: $249,996
State: CA