A perturbation-based estimate algorithm for parameters of coupled ordinary differential equations, applications from chemical reactions to metabolic dynamics

Conversion of complex phenomena in medicine, pharmaceutical and systems biology fields to a system of ordinary differential equations (ODEs) and identification of parameters from experimental data and theoretical model equations can be treated as a computational engine to arrive at the best solution for chemical reactions, biochemical metabolic and intracellular pathways. Particularly, to gain insight into the pathophysiology of diabetes's metabolism in our current clinical studies, glucose kinetics and insulin secretion can be assessed by the ODE model.Parameter estimation is usually performed by minimizing a cost function which quantifies the difference between theoretical model predictions and experimental measurements. This paper explores how the numerical method and iteration program are developed to search ODE's parameters using the perturbation method, instead of the Gauss–Newton or Levenberg–Marquardt method. Several interesting applications, including Lotka–Volterra chemical reaction system, Lorenz chaos, dynamics of tetracycline hydrochloride concentration, and Bergman's Minimal Model for glucose kinetics are illustrated.