Infectious Diseases Modeling Toolbox

Meeting Times:

• Wednesday, July 16, 1:30 PM – 5:00 PM
• Thursday July 17, 9:00 AM – 5:00 PM
• Friday July 18, 9:00 AM – 5:00 PM

Classroom: TBA

Module Summary:

Mathematical models built on systems of ordinary differential equations (ODEs) are widely utilized across diverse scientific disciplines to rigorously test hypotheses, determine essential model parameters, and produce reliable predictions about system dynamics. This module provides participants with a deep, integrated understanding of model fitting, parameter estimation, identifiability analysis, and calibration techniques—core pillars of comprehensive model development. To support these applications, this module introduces both frequentist and Bayesian approaches for estimating parameters and generating short-term forecasts with explicit uncertainty quantification from dynamical models, drawing on real-world examples from epidemic modeling scenarios of varying complexity.

Building on this foundation, the course emphasizes the application of frequentist and Bayesian approaches to parameter estimation and the generation of forecasts. Specifically, participants will learn to leverage QuantDiffForecast, a MATLAB toolbox specifically tailored for parameter estimation and short-term forecasting of ODE-based dynamical models. QuantDiffForecast accommodates multiple error structures (e.g., Poisson, negative binomial) and employs techniques like parametric bootstrapping to rigorously quantify uncertainty in forecasts. Additionally, participants will explore BayesianFitForecast, an R toolbox that streamlines Bayesian parameter estimation and forecasting in ODE-driven models. It automatically generates Stan code for Bayesian inference, enabling users to estimate parameters, assess uncertainty, and forecast outcomes with flexible prior specifications. The module will alternate between lectures and computer labs, offering hands-on opportunities to apply these methods to real-world models and datasets.

Prerequisites:
This module assumes knowledge of probability and inference covered in an introductory statistical course. Students will learn to use R and MATLAB toolboxes designed for parameter estimation and forecasting using dynamic models. Students are expected to have basic knowledge of the R computing environment. Students new to R should complete a tutorial before the module.

Module Content:

• Brief review of ordinary differential equation models, with a focus on their application to infectious disease transmission, control, and parameter estimation.
• Introduction to parameter identifiability, highlighting its importance in ensuring reliable model predictions and interpretations.
• Introduction to uncertainty quantification using parametric bootstrapping.
• Methods for model selection and assessing the quality of model fit.
• Bayesian estimation framework for fitting and forecasting epidemic trajectories with an emphasis on calibration and validation techniques.
• Model-based forecasts with quantified uncertainty.
• Metrics for assessing model calibration and forecasting performance.