Parameter Estimation of Stochastic Logistic Model: Levenberg Marquardt Method

Abstract

In this paper, we estimated the drift and diffusion parameters of the stochastic logistic models for the growth of Clostridium Acetobutylicum P262 using Levenberg-Marquardt optimization method of non linear least squares. The parameters are estimated for five different substrates. The solution of the deterministic models had been approximated using Fourth Order Runge-Kutta and for the solution of the stochastic differential equations, Milstein numerical scheme had been used. Small values of Mean Square Errors (MSE) of stochastic models indicated a good fit. Therefore the use of stochastic models are shown are appropriate in modelling cell growth of Clostridium Acetobutylicum P262, and precision for a certain distance of recording time. Keywords: Ito differential equation; stochastic logistic model; Levenberg Marquardt; Milstein scheme; fermentation