Fractional derivative model for tumor cells and immune system competition
| dc.citation.epage | 298 | |
| dc.citation.issue | 2 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 288 | |
| dc.contributor.affiliation | Університет Хасана ІІ Касабланки | |
| dc.contributor.affiliation | Hassan II of Casablanca University | |
| dc.contributor.author | Елкаф, М. | |
| dc.contributor.author | Аллалі, К. | |
| dc.contributor.author | Elkaf, M. | |
| dc.contributor.author | Allali, K. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T10:28:15Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | Моделювання динаміки складних біологічних захворювань, таких як рак, все ще є складною задачею. Отже, у нашому випадку намагаємося вивчити це, розглядаючи систему нормальних клітин, пухлинних клітин та імунну відповідь як математичні змінні, які є в структурі диференціальних рівнянь дробового порядку та виражають динаміку еволюції раку в умовах імунітету організму. Проаналізовано стійкість сформульованої системи в різних точках рівноваги. Чисельне моделювання виконується для отримання більш корисних і конкретних результатів щодо варіацій динаміки раку. | |
| dc.description.abstract | Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing. So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer’s evolution under immunity of the body. We will analyze the stability of the formulated system at different equilibrium points. Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer’s dynamics. | |
| dc.format.extent | 288-298 | |
| dc.format.pages | 11 | |
| dc.identifier.citation | Elkaf M. Fractional derivative model for tumor cells and immune system competition / M. Elkaf, K. Allali // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 288–298. | |
| dc.identifier.citationen | Elkaf M. Fractional derivative model for tumor cells and immune system competition / M. Elkaf, K. Allali // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 288–298. | |
| dc.identifier.doi | 10.23939/mmc2023.02.288 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63421 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 2 (10), 2023 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 2 (10), 2023 | |
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| dc.relation.references | [4] Sol´ıs–P´erez J., G´omez–Aguilar J., Atangana A. A fractional mathematical model of breast cancer competition model. Chaos, Solitons & Fractals. 127, 38–54 (2019). | |
| dc.relation.references | [5] El Alami laaroussi A., El Hia M., Rachik M., Ghazzali R. Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy. Computational and Mathematical Methods in Medicine. 2019, 1732815 (2019). | |
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| dc.relation.references | [7] Kang H.-W., Crawford M., Fabbri M., Nuovo G., Garofalo M., Nana-Sinkam S. P., Friedman A. A mathematical model for microRNA in lung cancer. PloS One. 8 (1), e53663 (2013). | |
| dc.relation.references | [8] Danane J., Hammouch Z., Allali K., Rashid S., Singh J. A fractional-order model of coronavirus disease 2019 (COVID-19) with governmental action and individual reaction. Mathematical Methods in the Applied Sciences. 1–14 (2021). | |
| dc.relation.references | [9] Danane J., Allali K., Hammouch Z. Mathematical analysis of a fractional differential model of HBV infection with antibody immune response. Chaos, Solitons & Fractals. 136, 109787 (2020). | |
| dc.relation.references | [10] Kumar P., Erturk V. S., Yusuf A., Kumar S. Fractional time-delay mathematical modeling of Oncolytic Virotherapy. Chaos, Solitons & Fractals. 150, 111123 (2021). | |
| dc.relation.references | [11] Pawar D. D., Patil W. D., Raut D. K. Fractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India. Mathematical Modeling and Computing. 8 (2), 253–266 (2021). | |
| dc.relation.references | [12] Miller K. S., Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley–Interscience (1993). | |
| dc.relation.references | [13] Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M. A fractional-order model for drinking alcohol behaviour leading to road accidents and violence. Mathematical Modeling and Computing. 9 (3), 501–518 (2022). | |
| dc.relation.references | [14] Allali K. Stability analysis and optimal control of HPV infection model with early-stage cervical cancer. Biosystems. 199, 104321 (2021). | |
| dc.relation.references | [15] Bretti G., De Ninno A., Natalini R., Peri D., Roselli N. Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment. Axioms. 10 (4), 243 (2021). | |
| dc.relation.references | [16] Paterson C., Clevers H., Bozic I. Mathematical model of colorectal cancer initiation. Proceedings of the National Academy of Sciences. 117 (34), 20681–20688 (2020). | |
| dc.relation.references | [17] Fadugba S. E., Ali F., Abubakar A. B. Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order. Mathematical Modeling and Computing. 8 (3), 537–548 (2021). | |
| dc.relation.references | [18] Ozdemir N., U¸car E. Investigating of an immune system-cancer mathematical model with Mittag–Leffler ¨ kernel. AIMS Mathematics. 5 (2), 1519–1531 (2020). | |
| dc.relation.references | [19] Amine S., Hajri Y., Allali K. A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation. Chaos, Solitons & Fractals. 161, 112396 (2022). | |
| dc.relation.references | [20] Alharbi S. A., Rambely A. S. A New ODE-Based Model for Tumor Cells and Immune System Competition. Mathematics. 8 (8), 1285 (2020). | |
| dc.relation.references | [21] Lin W. Global existence theory and chaos control of fractional differential equations. Journal of Mathematical Analysis and Applications. 332 (1), 709–726 (2007). | |
| dc.relation.references | [22] Matignon D. Stability results for fractional differential equations with applications to control processing. Computational Engineering in Systems Applications. 2, 963–968 (1996). | |
| dc.relation.references | [23] Atangana A., Owolabi K. M. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena. 13 (1), 3 (2018). | |
| dc.relation.references | [24] Garrappa R. On linear stability of predictor–corrector algorithms for fractional differential equations. International Journal of Computer Mathematics. 87 (10), 2281–2290 (2010). | |
| dc.relation.referencesen | [1] Pearson–Stuttard J., Zhou B., Kontis V., Bentham J., Gunter M. J., Ezzati M. Retracted: Worldwide burden of cancer attributable to diabetes and high body-mass index: a comparative risk assessment. The Lancet Diabetes & Endocrinology. 6 (2), 95–104 (2018). | |
| dc.relation.referencesen | [2] Addi R. A., Benksim A., Cherkaoui M. Vulnerability of people with cancer and the potential risks of COVID-19 Pandemic: A perspective in Morocco. Signa Vitae. 16 (1), 207–208 (2020). | |
| dc.relation.referencesen | [3] Gabriel J. A. The Biology of Cancer. John Wiley & Sons (2007). | |
| dc.relation.referencesen | [4] Sol´ıs–P´erez J., G´omez–Aguilar J., Atangana A. A fractional mathematical model of breast cancer competition model. Chaos, Solitons & Fractals. 127, 38–54 (2019). | |
| dc.relation.referencesen | [5] El Alami laaroussi A., El Hia M., Rachik M., Ghazzali R. Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy. Computational and Mathematical Methods in Medicine. 2019, 1732815 (2019). | |
| dc.relation.referencesen | [6] Lai X., Friedman A. Exosomal miRs in lung cancer: A mathematical model. PLoS One. 11 (12), e0167706 (2016). | |
| dc.relation.referencesen | [7] Kang H.-W., Crawford M., Fabbri M., Nuovo G., Garofalo M., Nana-Sinkam S. P., Friedman A. A mathematical model for microRNA in lung cancer. PloS One. 8 (1), e53663 (2013). | |
| dc.relation.referencesen | [8] Danane J., Hammouch Z., Allali K., Rashid S., Singh J. A fractional-order model of coronavirus disease 2019 (COVID-19) with governmental action and individual reaction. Mathematical Methods in the Applied Sciences. 1–14 (2021). | |
| dc.relation.referencesen | [9] Danane J., Allali K., Hammouch Z. Mathematical analysis of a fractional differential model of HBV infection with antibody immune response. Chaos, Solitons & Fractals. 136, 109787 (2020). | |
| dc.relation.referencesen | [10] Kumar P., Erturk V. S., Yusuf A., Kumar S. Fractional time-delay mathematical modeling of Oncolytic Virotherapy. Chaos, Solitons & Fractals. 150, 111123 (2021). | |
| dc.relation.referencesen | [11] Pawar D. D., Patil W. D., Raut D. K. Fractional-order mathematical model for analysing impact of quarantine on transmission of COVID-19 in India. Mathematical Modeling and Computing. 8 (2), 253–266 (2021). | |
| dc.relation.referencesen | [12] Miller K. S., Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley–Interscience (1993). | |
| dc.relation.referencesen | [13] Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M. A fractional-order model for drinking alcohol behaviour leading to road accidents and violence. Mathematical Modeling and Computing. 9 (3), 501–518 (2022). | |
| dc.relation.referencesen | [14] Allali K. Stability analysis and optimal control of HPV infection model with early-stage cervical cancer. Biosystems. 199, 104321 (2021). | |
| dc.relation.referencesen | [15] Bretti G., De Ninno A., Natalini R., Peri D., Roselli N. Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment. Axioms. 10 (4), 243 (2021). | |
| dc.relation.referencesen | [16] Paterson C., Clevers H., Bozic I. Mathematical model of colorectal cancer initiation. Proceedings of the National Academy of Sciences. 117 (34), 20681–20688 (2020). | |
| dc.relation.referencesen | [17] Fadugba S. E., Ali F., Abubakar A. B. Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order. Mathematical Modeling and Computing. 8 (3), 537–548 (2021). | |
| dc.relation.referencesen | [18] Ozdemir N., U¸car E. Investigating of an immune system-cancer mathematical model with Mittag–Leffler ¨ kernel. AIMS Mathematics. 5 (2), 1519–1531 (2020). | |
| dc.relation.referencesen | [19] Amine S., Hajri Y., Allali K. A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation. Chaos, Solitons & Fractals. 161, 112396 (2022). | |
| dc.relation.referencesen | [20] Alharbi S. A., Rambely A. S. A New ODE-Based Model for Tumor Cells and Immune System Competition. Mathematics. 8 (8), 1285 (2020). | |
| dc.relation.referencesen | [21] Lin W. Global existence theory and chaos control of fractional differential equations. Journal of Mathematical Analysis and Applications. 332 (1), 709–726 (2007). | |
| dc.relation.referencesen | [22] Matignon D. Stability results for fractional differential equations with applications to control processing. Computational Engineering in Systems Applications. 2, 963–968 (1996). | |
| dc.relation.referencesen | [23] Atangana A., Owolabi K. M. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena. 13 (1), 3 (2018). | |
| dc.relation.referencesen | [24] Garrappa R. On linear stability of predictor–corrector algorithms for fractional differential equations. International Journal of Computer Mathematics. 87 (10), 2281–2290 (2010). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.subject | моделювання раку | |
| dc.subject | імунна відповідь | |
| dc.subject | дробовий порядок | |
| dc.subject | стійкість | |
| dc.subject | числовий розв’язок | |
| dc.subject | cancer modeling | |
| dc.subject | immune response | |
| dc.subject | fractional-order | |
| dc.subject | stability | |
| dc.subject | numerical solution | |
| dc.title | Fractional derivative model for tumor cells and immune system competition | |
| dc.title.alternative | Модель конкуренції пухлинних клітин та імунної системи з дробовими похідними | |
| dc.type | Article |
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