Stochastic differential equation for two-phase growth model

Most mathematical models to describe natural phenomena in ecology are models with single-phase. 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...

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Main Author:	Granita, Granita
Format:	Thesis
Language:	English
Published:	2018
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/79116/1/GranitaPFS2018.pdf
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spelling	my-utm-ep.791162018-09-30T08:17:24Z Stochastic differential equation for two-phase growth model 2018 Granita, Granita QA Mathematics Most mathematical models to describe natural phenomena in ecology are models with single-phase. 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 two-phase models because their growth can be divided into two phases, even more, each phase requires different growth models. Most two-phase models are presented in the form of deterministic models, since two-phase models using stochastic approach have not been extensively studied. In previous study, Zheng’s two-phase 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 two-phase 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 second-phase is complicated to be determined. Thus, two-phase growth models are often difficult to build. To overcome this problem, stochastic differential equation (SDE) for two-phase growth model is proposed in this study. The SDE for BDPs is derived from CTMC for each phase, via Fokker-Planck equations. The SDE for twophase population growth model developed in this study is intended to be an alternative to the two-phase models of CTMC population model, since the significance of the SDE model is simpler to construct, and it gives closer approximation to real data. 2018 Thesis http://eprints.utm.my/id/eprint/79116/ http://eprints.utm.my/id/eprint/79116/1/GranitaPFS2018.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Granita, Granita Stochastic differential equation for two-phase growth model
description	Most mathematical models to describe natural phenomena in ecology are models with single-phase. 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 two-phase models because their growth can be divided into two phases, even more, each phase requires different growth models. Most two-phase models are presented in the form of deterministic models, since two-phase models using stochastic approach have not been extensively studied. In previous study, Zheng’s two-phase 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 two-phase 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 second-phase is complicated to be determined. Thus, two-phase growth models are often difficult to build. To overcome this problem, stochastic differential equation (SDE) for two-phase growth model is proposed in this study. The SDE for BDPs is derived from CTMC for each phase, via Fokker-Planck equations. The SDE for twophase population growth model developed in this study is intended to be an alternative to the two-phase models of CTMC population model, since the significance of the SDE model is simpler to construct, and it gives closer approximation to real data.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Granita, Granita
author_facet	Granita, Granita
author_sort	Granita, Granita
title	Stochastic differential equation for two-phase growth model
title_short	Stochastic differential equation for two-phase growth model
title_full	Stochastic differential equation for two-phase growth model
title_fullStr	Stochastic differential equation for two-phase growth model
title_full_unstemmed	Stochastic differential equation for two-phase growth model
title_sort	stochastic differential equation for two-phase growth model
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2018
url	http://eprints.utm.my/id/eprint/79116/1/GranitaPFS2018.pdf
_version_	1747818150478479360

Stochastic differential equation for two-phase growth model

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