Granita, Granita (2018) Stochastic differential equation for twophase growth model. PhD thesis, Universiti Teknologi Malaysia, Faculty of Science.

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Abstract
Most mathematical models to describe natural phenomena in ecology are models with singlephase. The models are created as such to represent the phenomena as realistic as possible such as logistic models with different types. However, several phenomena in population growth such as embryos, cells and human are better approximated by twophase models because their growth can be divided into two phases, even more, each phase requires different growth models. Most twophase models are presented in the form of deterministic models, since twophase models using stochastic approach have not been extensively studied. In previous study, Zheng’s twophase growth model had been implemented in continuous time Markov chain (CTMC). It assumes that the population growth follows Yule process before the critical size, and the Prendiville process after that. In this research, Zheng’s twophase growth model has been modified into two new models. Generally, probability distribution of birth and death processes (BDPs) of CTMC is intractable; and even if its first–passage time distribution can be obtained, the conditional distribution for the secondphase is complicated to be determined. Thus, twophase growth models are often difficult to build. To overcome this problem, stochastic differential equation (SDE) for twophase growth model is proposed in this study. The SDE for BDPs is derived from CTMC for each phase, via FokkerPlanck equations. The SDE for twophase population growth model developed in this study is intended to be an alternative to the twophase models of CTMC population model, since the significance of the SDE model is simpler to construct, and it gives closer approximation to real data.
Item Type:  Thesis (PhD) 

Additional Information:  Thesis (Doktor Falsafah (Matematik))  Universiti Teknologi Malaysia, 2018; Supervisor : Dr. Arifah Bahar 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  79116 
Deposited By:  Widya Wahid 
Deposited On:  30 Sep 2018 08:17 
Last Modified:  30 Sep 2018 08:17 
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