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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Universiti Kebangsaan Malaysia
2015
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| Online Access: | http://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/1/11_Mazma_Syahidatul.pdf |
| _version_ | 1848811964079276032 |
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| 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, |
| building | UKM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T23:54:45Z |
| format | Article |
| id | oai:generic.eprints.org:9045 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T23:54:45Z |
| publishDate | 2015 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org: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 |
| spellingShingle | Mazma Syahidatul Ayuni Mazlan, Norhayati Rosli, Nina Suhaity Azmi, Arifah Bahar, Modelling the cervical cancer growth process by stochastic delay differential equations |
| title | 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_short | Modelling the cervical cancer growth process by
stochastic delay differential equations |
| title_sort | modelling the cervical cancer growth process by
stochastic delay differential equations |
| url | http://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/ http://journalarticle.ukm.my/9045/1/11_Mazma_Syahidatul.pdf |