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Modeling with Differential Equations

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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

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Related Experiment Video

Updated: Jan 15, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

BayesianFitForecast: a user-friendly R toolbox for parameter estimation and forecasting with ordinary differential

Hamed Karami¹, Amanda Bleichrodt², Ruiyan Luo²

¹Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA.

BMC Medical Informatics and Decision Making

|October 15, 2025

Summary

This summary is machine-generated.

BayesianFitForecast is a new R toolbox simplifying Bayesian parameter estimation and forecasting for ordinary differential equation (ODE) models. It lowers the coding barrier for complex dynamical systems, enhancing public health and epidemiological decision-making.

Keywords:

Bayesian calibration Bayesian inference Epidemiological modeling Forecasting Hamiltonian Monte Carlo MCMC sampling Model selection ODE parameter estimation Stan R interface Uncertainty quantification

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Area of Science:

Computational Biology and Bioinformatics
Epidemiology and Public Health
Mathematical Modeling

Background:

Ordinary differential equations (ODEs) are crucial for modeling dynamic systems in science and healthcare.
Bayesian calibration and forecasting for ODE models often demand extensive coding expertise.
A need exists for accessible tools to facilitate Bayesian inference in dynamical systems.

Purpose of the Study:

Introduce BayesianFitForecast, a user-friendly R toolbox.
Streamline Bayesian parameter estimation and forecasting for ODE models.
Reduce the technical barrier for applying Bayesian methods in health informatics and public health.

Main Methods:

Automated generation of Stan files for ODE models.
User-friendly interface for model configuration and prior definition.
Application to historical epidemic datasets (e.g., 1918 influenza, 1896 Bombay plague) and simulated data.
Evaluation of parameter estimation and forecasting performance.

Main Results:

Demonstrated robust parameter estimation and forecasting.
Successful application to real-world and simulated epidemic data.
Validated performance under different observation error structures (Poisson, negative binomial).
Provided comprehensive model performance evaluation tools.

Conclusions:

Enhanced accessibility of advanced Bayesian methods for time-series modeling and forecasting.
Broadened applications in healthcare forecasting and epidemiological studies.
Included an interactive Shiny web application and tutorial video for user support.