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 Gompertz...
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my.utm.585852021-09-12T07:33:52Z http://eprints.utm.my/id/eprint/58585/ Modelling the cervical cancer growth process by stochastic delay differential equations Mazlan,, M. S. A. Rosli, N. Azmi, N. S. Bahar, A. 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. Penerbit UTM Press 2015 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/58585/1/MazmaSyahidatulAyuni2015_ModellingtheCervicalCancerGrowth.pdf Mazlan,, M. S. A. and Rosli, N. and Azmi, N. S. and Bahar, A. (2015) Modelling the cervical cancer growth process by stochastic delay differential equations. Sains Malaysia, 44 (8). pp. 1153-1157. ISSN 1266-039 http://dx.doi.org/10.17576/jsm-2015-4408-11 DOI: 10.17576/jsm-2015-4408-11 |
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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. |
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Article |
author |
Mazlan,, M. S. A. Rosli, N. Azmi, N. S. Bahar, A. |
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Mazlan,, M. S. A. Rosli, N. Azmi, N. S. Bahar, A. |
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Mazlan,, M. S. A. |
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 |
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Penerbit UTM Press |
publishDate |
2015 |
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http://eprints.utm.my/id/eprint/58585/1/MazmaSyahidatulAyuni2015_ModellingtheCervicalCancerGrowth.pdf http://eprints.utm.my/id/eprint/58585/ http://dx.doi.org/10.17576/jsm-2015-4408-11 |
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