Parameter identifiability, parameter estimation and model prediction for differential equation models

TL;DR

This paper introduces computational tools for assessing parameter identifiability, estimating parameters, and generating model predictions in differential equation models, using a likelihood-based approach with open-source code support.

Contribution

It presents a unified likelihood-based framework and computational exercises for parameter analysis in differential equation models, supported by accessible open-source tools.

Findings

Tools for parameter identifiability assessment

Algorithms for parameter estimation

Methods for model prediction generation

Abstract

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model parameters. This question is closely related to the concept of parameter identifiability, and in this article we present a series of computational exercises to introduce tools that can be used to assess parameter identifiability, estimate parameters and generate model predictions. Taking a likelihood-based approach, we show that very similar ideas and algorithms can be used to deal with a range of different mathematical modeling frameworks. The exercises and results presented in this article are supported by a suite of open access codes that can be accessed on GitHub.