Stability analysis of radiotherapy cancer treatment model with fractional derivative
This paper presents the condition for uniqueness, the stability analysis, and the bifurcation analysis of a mathematical model that simulates a radiotherapy cancer treatment process. The presented model was the previous cancer treatment model integrated with the Caputo fractional derivative and th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2020
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| Online Access: | http://journalarticle.ukm.my/16013/ http://journalarticle.ukm.my/16013/1/22.pdf |
| _version_ | 1848813942632087552 |
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| author | Musiliu Folarin Farayol, Sharidan Shafie, Fuaada Mohd Siam, |
| author_facet | Musiliu Folarin Farayol, Sharidan Shafie, Fuaada Mohd Siam, |
| author_sort | Musiliu Folarin Farayol, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | This paper presents the condition for uniqueness, the stability analysis, and the bifurcation analysis of a mathematical
model that simulates a radiotherapy cancer treatment process. The presented model was the previous cancer treatment
model integrated with the Caputo fractional derivative and the Linear-Quadratic with the repopulation model. The
metric space analysis was used to establish the conditions for the presence of unique fixed points for the model,
which indicated the presence of unique solutions. After establishing uniqueness, the model was used to simulate the
fractionated treatment process of six cancer patients treated with radiotherapy. The simulations of the cancer
treatment process were done in MATLAB with numerical and radiation parameters. The numerical parameters were
obtained from previous literature and the radiation parameters were obtained from reported clinical data. The solutions
of the simulations represented the final volumes of tumors and normal cells. Subsequently, the initial values of the model
were varied with 200 different values for each patient and the corresponding solutions were recorded. The continuity
of the solutions was used to investigate the stability of the solutions with respect to initial values. In addition, the value
of the Caputo fractional derivative was chosen as the bifurcation parameter. This parameter was varied with 500
different values to determine the bifurcation values. It was concluded that the solutions are unique and stable, hence the
model is well-posed. Therefore, it can be used to simulate a cancer treatment process as well as to predict outcomes of
other radiation protocols. |
| first_indexed | 2025-11-15T00:26:12Z |
| format | Article |
| id | oai:generic.eprints.org:16013 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:26:12Z |
| publishDate | 2020 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:160132020-12-17T05:17:12Z http://journalarticle.ukm.my/16013/ Stability analysis of radiotherapy cancer treatment model with fractional derivative Musiliu Folarin Farayol, Sharidan Shafie, Fuaada Mohd Siam, This paper presents the condition for uniqueness, the stability analysis, and the bifurcation analysis of a mathematical model that simulates a radiotherapy cancer treatment process. The presented model was the previous cancer treatment model integrated with the Caputo fractional derivative and the Linear-Quadratic with the repopulation model. The metric space analysis was used to establish the conditions for the presence of unique fixed points for the model, which indicated the presence of unique solutions. After establishing uniqueness, the model was used to simulate the fractionated treatment process of six cancer patients treated with radiotherapy. The simulations of the cancer treatment process were done in MATLAB with numerical and radiation parameters. The numerical parameters were obtained from previous literature and the radiation parameters were obtained from reported clinical data. The solutions of the simulations represented the final volumes of tumors and normal cells. Subsequently, the initial values of the model were varied with 200 different values for each patient and the corresponding solutions were recorded. The continuity of the solutions was used to investigate the stability of the solutions with respect to initial values. In addition, the value of the Caputo fractional derivative was chosen as the bifurcation parameter. This parameter was varied with 500 different values to determine the bifurcation values. It was concluded that the solutions are unique and stable, hence the model is well-posed. Therefore, it can be used to simulate a cancer treatment process as well as to predict outcomes of other radiation protocols. Penerbit Universiti Kebangsaan Malaysia 2020-11 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/16013/1/22.pdf Musiliu Folarin Farayol, and Sharidan Shafie, and Fuaada Mohd Siam, (2020) Stability analysis of radiotherapy cancer treatment model with fractional derivative. Sains Malaysiana, 49 (11). pp. 2833-2846. ISSN 0126-6039 https://www.ukm.my/jsm/malay_journals/jilid49bil11_2020/KandunganJilid49Bil11_2020.html |
| spellingShingle | Musiliu Folarin Farayol, Sharidan Shafie, Fuaada Mohd Siam, Stability analysis of radiotherapy cancer treatment model with fractional derivative |
| title | Stability analysis of radiotherapy cancer treatment model with fractional derivative |
| title_full | Stability analysis of radiotherapy cancer treatment model with fractional derivative |
| title_fullStr | Stability analysis of radiotherapy cancer treatment model with fractional derivative |
| title_full_unstemmed | Stability analysis of radiotherapy cancer treatment model with fractional derivative |
| title_short | Stability analysis of radiotherapy cancer treatment model with fractional derivative |
| title_sort | stability analysis of radiotherapy cancer treatment model with fractional derivative |
| url | http://journalarticle.ukm.my/16013/ http://journalarticle.ukm.my/16013/ http://journalarticle.ukm.my/16013/1/22.pdf |