Parameter Estimation of Stochastic Logistic Model: Levenberg-Marquardt Method

Abstract In this paper, we estimate the drift and diffusion parameters of the stochas-tic logistic models for the growth of ClostridiumAcetobutylicum P262 using Levenberg-Marquardt optimization method of non linear least squares. The parameters are esti-mated for five different substrates. The solution of the deterministic models has been approximated using Fourth Order Runge-Kutta and for the solution of the stochastic differential equations, Milstein numerical scheme has been used. Small values of Mean Square Errors (MSE) of stochastic models indicate good fits. Therefore the use of stochastic models are shown to be appropriate in modelling cell growth of Clostridium Acetobutylicum P262