Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations

In this paper, the uncontrolled environmental factors are perturbed into the growth rate deceleration factor of the Gompertzian deterministic model. The growth process under Gompertz’s law is considered, thus lead to stochastic differential equations of Gompertzian with time delay. The Gompertzian d...

Full description

Bibliographic Details
Main Authors:	Mazma Syahidatul Ayuni, Mazlan, Norhayati, Rosli, Nina Suhaity, Azmi, Arifah, Bahar
Format:	Article
Language:	English English
Published:	Universiti Kebangsaan Malaysia 2015
Subjects:	QA Mathematics
Online Access:	http://umpir.ump.edu.my/id/eprint/12712/ http://umpir.ump.edu.my/id/eprint/12712/ http://umpir.ump.edu.my/id/eprint/12712/1/Sains%20Malaysiana%20Norhayati%20Rosli.pdf http://umpir.ump.edu.my/id/eprint/12712/7/fist-2015-hayati-Modelling%20the%20Cervical%20Cancer.pdf

id	ump-12712
recordtype	eprints
spelling	ump-127122018-01-25T02:30:40Z http://umpir.ump.edu.my/id/eprint/12712/ Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations Mazma Syahidatul Ayuni, Mazlan Norhayati, Rosli Nina Suhaity, Azmi Arifah, Bahar QA Mathematics In this paper, the uncontrolled environmental factors are perturbed into the growth rate deceleration factor of the Gompertzian deterministic model. The growth process under Gompertz’s law is considered, thus lead to stochastic differential equations of Gompertzian with time delay. The Gompertzian deterministic model has proven to fit well with the clinical data of cancerous growth, however the performance of stochastic model towards clinical data is yet to be confirmed. The prediction quality of stochastic model is evaluated by comparing the simulated results with the clinical data of cervical cancer growth. The parameter estimation of stochastic models is computed by using simulated maximum likelihood method. 4-stage stochastic Runge-Kutta is applied to simulate the solution of stochastic model. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits. Universiti Kebangsaan Malaysia 2015-08 Article PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/12712/1/Sains%20Malaysiana%20Norhayati%20Rosli.pdf application/pdf en http://umpir.ump.edu.my/id/eprint/12712/7/fist-2015-hayati-Modelling%20the%20Cervical%20Cancer.pdf Mazma Syahidatul Ayuni, Mazlan and Norhayati, Rosli and Nina Suhaity, Azmi and Arifah, Bahar (2015) Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations. Sains Malaysiana, 44 (8). pp. 1153-1157. ISSN 0126-6039 http://www.ukm.my/jsm/pdf_files/SM-PDF-44-8-2015/11%20Mazma%20Syahidatul.pdf
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Malaysia Pahang
building	UMP Institutional Repository
collection	Online Access
language	English English
topic	QA Mathematics
spellingShingle	QA Mathematics Mazma Syahidatul Ayuni, Mazlan Norhayati, Rosli Nina Suhaity, Azmi Arifah, Bahar Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations
description	In this paper, the uncontrolled environmental factors are perturbed into the growth rate deceleration factor of the Gompertzian deterministic model. The growth process under Gompertz’s law is considered, thus lead to stochastic differential equations of Gompertzian with time delay. The Gompertzian deterministic model has proven to fit well with the clinical data of cancerous growth, however the performance of stochastic model towards clinical data is yet to be confirmed. The prediction quality of stochastic model is evaluated by comparing the simulated results with the clinical data of cervical cancer growth. The parameter estimation of stochastic models is computed by using simulated maximum likelihood method. 4-stage stochastic Runge-Kutta is applied to simulate the solution of stochastic model. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.
format	Article
author	Mazma Syahidatul Ayuni, Mazlan Norhayati, Rosli Nina Suhaity, Azmi Arifah, Bahar
author_facet	Mazma Syahidatul Ayuni, Mazlan Norhayati, Rosli Nina Suhaity, Azmi Arifah, Bahar
author_sort	Mazma Syahidatul Ayuni, Mazlan
title	Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations
title_short	Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations
title_full	Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations
title_fullStr	Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations
title_full_unstemmed	Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations
title_sort	modelling the cervical cancer growth process by stochastic delay differential equations
publisher	Universiti Kebangsaan Malaysia
publishDate	2015
url	http://umpir.ump.edu.my/id/eprint/12712/ http://umpir.ump.edu.my/id/eprint/12712/ http://umpir.ump.edu.my/id/eprint/12712/1/Sains%20Malaysiana%20Norhayati%20Rosli.pdf http://umpir.ump.edu.my/id/eprint/12712/7/fist-2015-hayati-Modelling%20the%20Cervical%20Cancer.pdf
first_indexed	2023-09-18T22:14:35Z
last_indexed	2023-09-18T22:14:35Z
_version_	1777415251676889088

Modelling the Cervical Cancer Growth Process by Stochastic Delay Differential Equations

Similar Items