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...

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Main Authors:	Mazma Syahidatul Ayuni Mazlan, Norhayati Rosli, Nina Suhaity Azmi, Arifah Bahar
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2015
Online Access:	http://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/1/11_Mazma_Syahidatul.pdf

id	ukm-9045
recordtype	eprints
spelling	ukm-90452016-12-14T06:48:49Z http://journalarticle.ukm.my/9045/ Modelling the cervical cancer growth process by stochastic delay differential equations Mazma Syahidatul Ayuni Mazlan, Norhayati Rosli, Nina Suhaity Azmi, Arifah Bahar, 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://journalarticle.ukm.my/9045/1/11_Mazma_Syahidatul.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 (4). pp. 1153-1157. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol44num8_2015/contentsVol44num8_2015.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
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,
spellingShingle	Mazma Syahidatul Ayuni Mazlan, Norhayati Rosli, Nina Suhaity Azmi, Arifah Bahar, Modelling the cervical cancer growth process by stochastic delay differential equations
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://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/1/11_Mazma_Syahidatul.pdf
first_indexed	2023-09-18T19:53:50Z
last_indexed	2023-09-18T19:53:50Z
_version_	1777406396652847104

Modelling the cervical cancer growth process by stochastic delay differential equations

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