Exploring Parameter Sensitivity Analysis in Mathematical Modeling with Ordinary Differential Equations

Authors

Viktoria Savatorova, Central Connecticut State UniversityFollow

Publication Date

10-10-2023

Keywords

parameter sensitivity, local and global sensitivity analysis, direct differential method, Pearson correlation coefficient, Spearman correlation coefficient, PRCC, Sobol indices, visualization techniques, fish population dynamics, harvesting.

Disciplines

Applied Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Statistics and Probability

Abstract

This paper presents an exploration into parameter sensitivity analysis in mathematical modeling using ordinary differential equations (ODEs). Taking the first steps in understanding local sensitivity analysis through the direct differential method and global sensitivity analysis using metrics like Pearson, Spearman, PRCC, and Sobol’, we provide readers with a basic understanding of parameter sensitivity analysis for mathematical modeling using ODEs. As an illustrative application, the system of differential equations modeling population dynamics of several fish species with harvest considerations is utilized. The results of employing local and global sensitivity analysis are compared, shedding light on the strengths and limitations of each approach. The paper serves as a starting point for readers interested in exploring parameter sensitivity in their mathematical models.

Recommended Citation

Savatorova, Viktoria (2023) "Exploring Parameter Sensitivity Analysis in Mathematical Modeling with Ordinary Differential Equations," CODEE Journal: Vol. 16, Article 4.
Available at: https://scholarship.claremont.edu/codee/vol16/iss1/4