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A practical introduction to ODE modelling in Stan for biological systems
Sara Hamis1, John Forslund1, Cici Chen Gu1
1Department of Information Technology, Uppsala University, Uppsala, Sweden.
Mathematical Biosciences
|July 23, 2026
Summary
This study introduces Stan, an open-source tool for mathematical biology, to estimate parameters in ordinary differential equation (ODE) models using Bayesian inference. It provides practical examples for analyzing biological systems with time series data.
Area of Science:
- Mathematical Biology
- Computational Statistics
- Biophysics
Background:
- Integrating dynamical systems models with time series data is crucial in mathematical biology.
- Numerous computational tools exist, with Stan being a prominent open-source probabilistic programming framework.
- Stan offers efficient Bayesian inference for parameter estimation, including built-in support for ordinary differential equation (ODE) models.
Purpose of the Study:
- To provide a practical, self-contained introduction to using Stan for parameter estimation and model evaluation of ODE models.
- To demonstrate applications with both toy models and real biological data.
- To explain the statistical methods underpinning Stan and computational Bayesian modeling in biology.
Main Methods:
- Utilizing Stan, a probabilistic programming framework, for computational Bayesian inference.
- Applying Stan's built-in mechanisms for ordinary differential equation (ODE) models.
- Illustrating parameter estimation and model evaluation for first-order linear and nonlinear ODEs through worked examples.
Main Results:
- Demonstrated successful parameter estimation for ODE models using Stan.
- Provided practical guidance through step-by-step examples with pedagogical and real-world datasets.
- Offered insights into the statistical foundations and computational aspects of Bayesian modeling in biology.
Conclusions:
- Stan is a powerful and accessible tool for mathematical biologists to perform parameter estimation and model evaluation for ODE models.
- The article serves as a practical guide for researchers applying computational Bayesian methods to biological data.
- Understanding Stan facilitates advanced analysis of dynamic biological systems.
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