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

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.