Parameter estimation of a two state delay differential equation modeling the human respiratory system

TL;DR

This paper investigates parameter estimation in a delay differential equation model of the human respiratory system, using numerical simulations and optimization algorithms to identify unknown parameters.

Contribution

It introduces a method for estimating parameters in a nonlinear delay differential equation model of respiration using Levenberg-Marquardt and Trust-region algorithms.

Findings

Successful parameter estimation from noisy data

Comparison of optimization algorithms for accuracy

Model effectively captures respiratory dynamics

Abstract

We study parameter estimation for the two state model which describes the balance equation for carbon dioxide and oxygen in human respiratory system. These are nonlinear parameter dependent and because of the transport delay in the respiratory control system, they are modeled with delay differential equation. Numerically simulated noisy data are generated and several examples are studied with Levenberg-Marquardt and Trust-region algorithms to determine the values of unknown parameters.