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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| Format: | Article |
| Language: | English English |
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Universiti Kebangsaan Malaysia
2015
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| Online Access: | 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 |
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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 | UMP 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 | 2025-11-15T01:51:20Z |
| format | Article |
| id | ump-12712 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T01:51:20Z |
| publishDate | 2015 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-127122023-04-11T04:47:38Z 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. (Published) http://www.ukm.my/jsm/pdf_files/SM-PDF-44-8-2015/11%20Mazma%20Syahidatul.pdf |
| 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 |
| 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 |
| topic | QA Mathematics |
| 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 |