Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262 - Tawfiqullah, Ayoubi (2015)
Ordinary differential equations (ODEs) and stochastic differential equations (SDEs) are widely used to model biological systems in the last decades. In both types of equations, the unknown function and its derivatives are evaluated at the same instant time, t. However, many of the natural phenomena do not have an immediate effect from the moment of their occurrence. For instance, a patient shows symptoms of an illness days or even weeks after the day in which they were infected. The dynamics of the systems differ if the corresponding characteristic equations involve time delay. Therefore, ODEs and SDEs which are simply depending on the present state are insufficient to explain this process. Such phenomenon can be modelled via stochastic delay differential equations (SDDEs). Batch fermentation process is one of the systems which subject to the presence of uncontrolled fluctuation and delayed feedback. ODEs and SDEs are not capable to model uncontrolled fluctuation and delayed feedback in fermentation process. It is necessary to model this process via SDDEs. Thus, this research is carried out to propose a stochastic model with delay effect for cell growth and solvent production of acetone and butanol by Clostridium Acetobutylicum P262 in fermentation process. The kinetic parameters of the results model are estimated via maximum likelihood method. The analytical solutions of this model is hard to be found, hence numerical method of 4-stage stochastic Runge-Kutta (SRK4) provide a way to simulate the solutions of the model. The RK4 and SRK4 methods are translated into C languages to obtain the numerical solutions of mathematical model for the cell growth concentration and solvents production. The experimental data is used to validate the results. The results indicate that the most suitable model to explain the solvent production by Clostridium Acetobutylicum P262 in fermentation process is SDDEs.