Proceedings of the Regional Conference on Statistical Sciences 2010 (RCSS’10) June 2010, 9-20 ISBN 978-967-363-157-5 © 2010 Malaysia Institute of Statistics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Malaysia 9 Stochastic Model of Gelatinised Sago Starch to Solvent Production by C. acetobutylicum P262. Norhayati Rosli 1 Arifah Bahar 1 Yeak Su Hoe 1 Haliza Abd.Rahman 1 1 Faculty of Science Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia E-mail: norhayati@ump.edu.my, arifah@utm.my, s.h.yeak@utm.my, haliza.ar@fs.utm.my Mohd Khairul Bazli Mohd Aziz 2 2 Fakulti Sains Komputer & Matematik Universiti Teknologi Mara Terenggganu, 23000 Dungun Terengganu E-mail: mkbazli@yahoo.com Madihah Md.Salleh 3 3 Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia Faculty of Bioscience and Bioengineering E-mail: madihah@fbb.utm.my ABSTRACT Fluctuations are inherent property of many physical systems in biology, epidemiology, finance and chemical reactions. They are recognized as unknown disturbances or stochastic effects. In order to describe the system embedded with the above effect, the system is modelled using stochastic differential equations (SDEs). This work is carried out to model the growth of C. acetobutylicum P262 in batch fermentation and solvent production using SDE. Since, the analytical solutions of this SDE are complex, a numerical simulation is applied to approximate the strong solution of the SDE. This paper also discusses the use of three different numerical methods in modelling the growth of C. acetobutylicum P262 and solvent production. Keywords: Stochastic Differential Equations, batch fermentation, Euler-Maruyama (EM), 2-stage Stochastic Runge-Kutta (SRK2), 4-stage Stochastic Runge-Kutta (SRK4). Introduction In a typical batch process the number of living cells varies with time. At zero time, the sterile nutrient solution in fermenter is inoculated with microorganism (C. acetobutylicum P262) and incubation is allowed to proceed under optimal physiological conditions. The microbial growth in gelatinized sago starch undergoes two distinct physiological stages (Madihah et al., 2008). The first stage is an acidogenic stage which involves an exponential growth phase. After a lag phase where no increase in cell numbers is evident, a period of rapid growth ensues and cell numbers increase exponentially with time. During exponential growth the pH culture decreases due to the production of acetic acid, butyric acid and hydrogen gas. The second phase has slow growth rate. This is a phase where the solvents (acetone and butanol) are produced. In this phase, both butyric acid and acetic acid are taken up by the bacterial cell to induce the transition to the solventogenic phase (Madihah, 2000). As time evolves, the system is subjected to an intrinsic variability of the competing within species and deviations from exponential growth arise (cell growth reach a stationary phase). It happens as a result of the nutrient level and toxin concentration achieves a value which can no longer support the maximum growth rate. These disturbances can be regarded as stochastic effects. Over last few decades, logistic and Luedeking-Piret equations had been used to model the solvent production by C. acetobutylicum P262. This model suffers several weaknesses. They lack of stochastic effect and give us no insight into the