Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262

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...

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Main Author:	Tawfiqullah, Ayoubi
Format:	Thesis
Language:	English
Published:	2015
Subjects:	TP Chemical technology
Online Access:	http://umpir.ump.edu.my/id/eprint/12624/19/Stochastic%20modelling%20of%20time%20delay%20for%20solvent%20production%20by%20Clostridium%20Acetobutylicum%20P262.pdf
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spelling	my-ump-ir.126242021-11-09T01:58:20Z Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262 2015-10 Tawfiqullah, Ayoubi TP Chemical technology 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. 2015-10 Thesis http://umpir.ump.edu.my/id/eprint/12624/ http://umpir.ump.edu.my/id/eprint/12624/19/Stochastic%20modelling%20of%20time%20delay%20for%20solvent%20production%20by%20Clostridium%20Acetobutylicum%20P262.pdf pdf en public masters Universiti Malaysia Pahang Faculty of Industrial Sciences and Technology
institution	Universiti Malaysia Pahang Al-Sultan Abdullah
collection	UMPSA Institutional Repository
language	English
topic	TP Chemical technology
spellingShingle	TP Chemical technology Tawfiqullah, Ayoubi Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262
description	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.
format	Thesis
qualification_level	Master's degree
author	Tawfiqullah, Ayoubi
author_facet	Tawfiqullah, Ayoubi
author_sort	Tawfiqullah, Ayoubi
title	Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262
title_short	Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262
title_full	Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262
title_fullStr	Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262
title_full_unstemmed	Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262
title_sort	stochastic modelling of time delay for solvent production by clostridium acetobutylicum p262
granting_institution	Universiti Malaysia Pahang
granting_department	Faculty of Industrial Sciences and Technology
publishDate	2015
url	http://umpir.ump.edu.my/id/eprint/12624/19/Stochastic%20modelling%20of%20time%20delay%20for%20solvent%20production%20by%20Clostridium%20Acetobutylicum%20P262.pdf
_version_	1783731968687472640

Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262

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