A simple mechanistic model for insulin-glucose-glucagon dynamics and its implications for diabetes management

Mackenzie Dalton; Emmanuel Asante-Asamani; James Greene; Mackenzie Dalton; Emmanuel Asante-Asamani; James Greene

doi:10.3934/mbe.2026060

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 6: 1651-1686. doi: 10.3934/mbe.2026060

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Research article

A simple mechanistic model for insulin-glucose-glucagon dynamics and its implications for diabetes management

Department of Mathematics, Clarkson University, NY 13699, USA

Received: 03 June 2025 Revised: 08 January 2026 Accepted: 15 February 2026 Published: 06 May 2026

Insulin and glucose dynamics are tightly regulated by the pancreatic islets of Langerhans, which contain beta cells that produce insulin and alpha cells that produce glucagon. Insulin lowers blood glucose by enabling cells to access glucose for energy, while glucagon raises blood glucose levels by stimulating the liver to produce glucose from non-carbohydrate sources as well as breaking down stored glycogen. Maintaining safe blood glucose levels is crucial, as both high (hyperglycemia) and low (hypoglycemia) levels can lead to life threatening consequences. In this work, a simple three-state mechanistic insulin-glucose-glucagon model is developed and validated using data from pigs subjected to an intravenous glucose tolerance test (IVGTT). The model is then used to investigate glucose and glucagon dynamics in patients administering exogenous insulin, shedding light on the impact of improper diabetes management. The results show that delayed administration of exogenous insulin increases the risk of hypoglycemia by suppressing glucagon production. Furthermore, insulin half-lives of 60 minutes or longer were tested, revealing that such prolonged exogenous insulin activity can suppress glucagon's response to critically low glucose levels. This finding suggests that shorter insulin half-lives may help reduce the risk of hypoglycemic events.
- glucagon,
- insulin,
- glucose,
- differential equations,
- diabetes,
- mathematical modeling
Citation: Mackenzie Dalton, Emmanuel Asante-Asamani, James Greene. A simple mechanistic model for insulin-glucose-glucagon dynamics and its implications for diabetes management[J]. Mathematical Biosciences and Engineering, 2026, 23(6): 1651-1686. doi: 10.3934/mbe.2026060

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Abstract

Insulin and glucose dynamics are tightly regulated by the pancreatic islets of Langerhans, which contain beta cells that produce insulin and alpha cells that produce glucagon. Insulin lowers blood glucose by enabling cells to access glucose for energy, while glucagon raises blood glucose levels by stimulating the liver to produce glucose from non-carbohydrate sources as well as breaking down stored glycogen. Maintaining safe blood glucose levels is crucial, as both high (hyperglycemia) and low (hypoglycemia) levels can lead to life threatening consequences. In this work, a simple three-state mechanistic insulin-glucose-glucagon model is developed and validated using data from pigs subjected to an intravenous glucose tolerance test (IVGTT). The model is then used to investigate glucose and glucagon dynamics in patients administering exogenous insulin, shedding light on the impact of improper diabetes management. The results show that delayed administration of exogenous insulin increases the risk of hypoglycemia by suppressing glucagon production. Furthermore, insulin half-lives of 60 minutes or longer were tested, revealing that such prolonged exogenous insulin activity can suppress glucagon's response to critically low glucose levels. This finding suggests that shorter insulin half-lives may help reduce the risk of hypoglycemic events.

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