SavedAdd your journal

Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2026 / Cilt: 40 Sayı: 2

Mathematical Modeling of Skin Cancer with the Effect of Stress

Cilt Kanserinin Stres Etkisiyle Matematiksel Modellenmesi

Şemsettin Tunca(ERCIYES UNIVERSITY)0000-0002-2149-2724
M. Tamer Senel(Erciyes University, Turkey)0000-0003-1915-5697
Fatma Özköse(ERCIYES UNIVERSITY)
Pages
429–449
Publication Date
2024-08-31
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The outcomes are expected to provide valuable insights to medical researchers in developing appropriate measures for screening and treating skin cancer.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper introduces a mathematical model for skin cancer, formulated by fractional order differential equations (FODE).
📊
Key Findings & Data:Considering the importance of the stress factor, it has been included in the model and its effect on tumor cells has been scrutinized.
💡
Conclusion & Impact:The outcomes are expected to provide valuable insights to medical researchers in developing appropriate measures for screening and treating skin cancer.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Kesirli MertebedenDiferansiyel Denklemler · Cilt Kanseri · Nümerik Simülasyonlar

Abstract

This paper introduces a mathematical model for skin cancer, formulated by fractional order differential equations (FODE). Considering the importance of the stress factor, it has been included in the model and its effect on tumor cells has been scrutinized. The study examines the local stability of equilibrium points and evaluates the impact of fractional derivatives on the dynamic behavior of the system. In addition, numerical simulations are conducted to analyze the influence of fractional order derivatives and distinct parameters on population dynamics. The presentation of graphs based on various fractional orders and parameter values aids in the visualization of the findings. The study further investigates the impact of stress on tumor cells. The outcomes are expected to provide valuable insights to medical researchers in developing appropriate measures for screening and treating skin cancer.

Özet

Bu çalışmada cilt kanseri için kesirli mertebeli diferansiyel denklemler (FODE)ile formüle edilen matematiksel bir model sunulmuştur. Stres faktörünün önemidikkate alınarak modele dahil edilmiş ve tümör hücreleri üzerindeki etkisiaraştırılmıştır. Denge noktalarının yerel kararlılığı incelenmiştir ve kesirlitürevlerin sistemin dinamik davranışı üzerindeki etkisi değerlendirilmiştir. Ekolarak, kesirli mertebeli türevlerin ve farklı parametrelerin popülasyondinamikleri üzerindeki etkisini analiz etmek için sayısal simülasyonlar yapılmıştır.Çeşitli kesirli mertebe ve parametre değerlerine dayalı grafiklerin sunulması,bulguların görselleştirilmesine yardımcı olmaktadır. Ayrıca stresin tümör hücreleriüzerindeki etkisi de araştırılmıştır. Sonuçların, tıbbi araştırmacılara cilt kanserinintaranması ve tedavisi için uygun önlemlerin geliştirilmesinde değerli bilgilersağlaması beklenmektedir.

🔖

Cite This Article

Tunca, Ş., Senel, M. T., Özköse, F. (2024). Mathematical Modeling of Skin Cancer with the Effect of Stress. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 40 Sayı: 2, 429–449. https://ajindex.com/articles/1266736

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (39)

  1. O'Sullivan, D. E., Brenner, D. R., Demers, P. A., Villeneuve, P. J., Friedenreich, C. M., King, W. D., & ComPARe Study Group. (2019). Indoor tanning and skin cancer in Canada: A meta-analysis and attributable burden estimation. Cancer epidemiology, 59, 1-7. Hylands P. Skin cancer: types, diagnosis and prevention. Heart Fail 2019;10. p. 00. Gray-Schopfer, V., Wellbrock, C., & Marais, R. (2007). Melanoma biology and new targeted therapy. Nature, 445(7130),851-857.
  2. Morgan, R. A., Dudley, M. E., Wunderlich, J. R., Hughes, M. S., Yang, J. C., Sherry, R. M.,. & Rosenberg, S. A. (2006). Cancer regression in patients after transfer of genetically engineered lymphocytes. Science, 314(5796),126-129.
  3. Nuzzo, C., Pino, M. S., & Cognetti, F. (2014). Systemic therapy in melanoma. Skin Cancer: A Practical Approach, 461-474. Kirkwood, J. M., Tarhini, A. A., Panelli, M. C., Moschos, S. J., Zarour, H. M., Butterfield, L. H., & Gogas, H. J. (2008). Next generation of immunotherapy for melanoma. Journal of Clinical Oncology, 26(20), 3445-3455.
  4. Dunn, G. P., Bruce, A. T., Ikeda, H., Old, L. J., & Schreiber, R. D. (2002). Cancer immunoediting: from immunosurveillance to tumor escape. Nature immunology, 3(11), 991-998. Fridman, W. H., Pagès, F., Sautès-Fridman, C., & Galon, J. (2012). The immune contexture in human tumours: impact on clinical outcome. Nature Reviews Cancer, 12(4), 298-306.
  5. Thomas, D. A., & Massagué, J. (2005). TGF- β directly targets cytotoxic T cell functions during tumor evasion of immune surveillance. Cancer cell, 8(5), 369-380.
  6. Moutsopoulos, N. M., Wen, J., & Wahl, S. M. (2008). TGF- β and tumors-an ill-fated alliance. Current opinion in immunology, 20(2), 234-240.
  7. Sun, H., Cao, D., Shen, K., Yang, J., Xiang, Y., Feng, F.,. & Song, L. (2018). Piver Type II vs. Type III hysterectomy in the treatment of early-stage cervical cancer: midterm follow-up results of a randomized controlled trial. Frontiers in Oncology, 8, 568.
  8. Dougan M, Dranoff G, Dougan SK. Cancer immunotherapy: beyond checkpoint blockade. Annu Rev Cancer Biol. (2018) 3:55-75. doi: 10.1146/ annurev-cancerbio-030518-055552
  9. Marelli, G., Howells, A., Lemoine, N. R., & Wang, Y. (2018). Oncolytic viral therapy and the immune system: a double-edged sword against cancer. Frontiers in immunology, 9, 866.
  10. Sabbar, Y., Yavuz, M., & Özköse, F. (2022). Infection Eradication Criterion in a General Epidemic Model with Logistic Growth, Quarantine Strategy, Media Intrusion, and Quadratic Perturbation. Mathematics, 10(22),4213. Weinberg, R. A. (2014). Coming full circle-from endless complexity to simplicity and back again. Cell, 157(1), 267-271. Kolch, W., Halasz, M., Granovskaya, M., & Kholodenko, B. N. (2015). The dynamic control of signal transduction networks in cancer cells. Nature Reviews Cancer, 15(9), 515-527. Eikenberry, S., Thalhauser, C., & Kuang, Y. (2009). Tumor-immune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma. PLoS computational biology, 5(4), e1000362.
  11. Pennisi, M. (2012). A mathematical model of immune-system-melanoma competition. Computational and mathematical methods in medicine, 2012. Nikolov, S., & Nenov, M. (2019). Modelling vaccine quantity in mathematical models of melanoma treatment. Series on Biomechanics.
  12. Shu, Y., Huang, J., Dong, Y., & Takeuchi, Y. (2020). Mathematical modeling and bifurcation analysis of pro- and anti-tumor macrophages. Applied Mathematical Modelling, 88, 758-773.
  13. Özköse, F., ŞENEL, M. T., & Habbireeh, R. (2021). Fractional-order mathematical modelling of cancer cells- cancer stem cells-immune system interaction with chemotherapy. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 67-83.
  14. Lai, X., & Friedman, A. (2017). Combination therapy for melanoma with BRAF/MEK inhibitor and immune checkpoint inhibitor: a mathematical model. BMC Systems Biology, 11(1), 1-18.
  15. Özköse, F., Yılmaz, S., Yavuz, M., Öztürk, İ., Şenel, M. T., Bağcı, B. Ş.,. & Önal, Ö. (2022). A fractional modeling of tumor-immune system interaction related to lung cancer with real data. The European Physical Journal Plus, 137, 1-28. Öztürk, I., & Özköse, F. (2020). Stability analysis of fractional order mathematical model of tumor-immune system interaction. Chaos, Solitons & Fractals, 133, 109614.
  16. Carvalho, A. R., Pinto, C., & Baleanu, D. (2018). HIV/HCV coinfection model: a fractional-order perspective for the effect of the HIV viral load. Advances in Difference Equations, 2018(1), 1-22.
  17. Podlubny I. Fractional differential equations. Academic Press, New York; 1999.
  18. Ghaziani, R. K., Alidousti, J., & Eshkaftaki, A. B. (2016). Stability and dynamics of a fractional order Leslie- Gower prey-predator model. Applied Mathematical Modelling, 40(3), 2075-2086.
  19. Petras I. Fractional -order nonlinear systems: modeling, analysis and simulation. London, Beijing: Springer; 2011.
  20. Baisad, K., & Moonchai, S. (2018). Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator-prey model with Allee effect and Holling type-III functional response. Advances in difference equations, 2018, 1-20. Ahmed, E., El-Sayed, A. M. A., & El-Saka, H. A. (2007). Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. Journal of Mathematical Analysis and Applications, 325(1), 542-553.
  21. Allen, L. J. An introduction to mathematical biology., 2007. ISBN, 10, 0-13.
  22. Özköse, F., Yavuz, M., Şenel, M. T., & Habbireeh, R. (2022). Fractional order modelling of omicron SARS-CoV- 2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons & Fractals, 157,111954.
  23. Özköse, F. (2023). Modeling of psoriasis by considering drug influence: A mathematical approach with memory trace. Computers in Biology and Medicine, 107791.
  24. Özköse, F. (2023). Long-Term Side Effects: A Mathematical Modeling of COVID-19 and Stroke with Real Data. Fractal and Fractional, 7(10),719.
  25. Özköse, F., Habbireeh, R., & Şenel, M. T. (2023). A novel fractional order model of SARS-CoV-2 and Cholera disease with real data. Journal of Computational and Applied Mathematics, 423, 114969.
  26. Diethelm, K., & Freed, A. D. (1998). The FracPECE subroutine for the numerical solution of differential equations of fractional order. Forschung und wissenschaftliches Rechnen, 1999, 57-71.
  27. Diethelm, K. (1997). An algorithm for the numerical solution of differential equations of fractional order. Electronic transactions on numerical analysis, 5(1), 1-6.
  28. Garrappa, R. (2010). On linear stability of predictor-corrector algorithms for fractional differential equations. International Journal of Computer Mathematics, 87(10), 2281-2290.
  29. Garrappa, R. (2018). Numerical solution of fractional differential equations: A survey and a software tutorial. Mathematics, 6(2), 16.
  30. Li, C., & Tao, C. (2009). On the fractional Adams method. Computers & Mathematics with Applications, 58(8),1573-1588.
  31. Rihan, F. A., & Velmurugan, G. (2020). Dynamics of fractional-order delay differential model for tumorimmune system. Chaos, Solitons & Fractals, 132, 109592.
  32. R.H. Thomlinson, Measurement and management of carcinoma of the breast. Clin.Radiol. 33(5), 481–493 (1982).
  33. Sarkar, R. R., & Banerjee, S. (2005). Cancer self remission and tumor stability–a stochastic approach. Mathematical Biosciences, 196(1), 65-81.
  34. Morgan, R. A., Dudley, M. E., Wunderlich, J. R., Hughes, M. S., Yang, J. C., Sherry, R. M.,. & Rosenberg, S. A. (2006). Cancer regression in patients after transfer of genetically engineered lymphocytes. Science, 314(5796),126-129.
  35. Sun, H., Cao, D., Shen, K., Yang, J., Xiang, Y., Feng, F.,. & Song, L. (2018). Piver Type II vs. Type III hysterectomy in the treatment of early-stage cervical cancer: midterm follow-up results of a randomized controlled trial. Frontiers in Oncology, 8, 568.
  36. Özköse, F., Yılmaz, S., Yavuz, M., Öztürk, İ., Şenel, M. T., Bağcı, B. Ş.,. & Önal, Ö. (2022). A fractional modeling of tumor-immune system interaction related to lung cancer with real data. The European Physical Journal Plus, 137, 1-28. Öztürk, I., & Özköse, F. (2020). Stability analysis of fractional order mathematical model of tumor-immune system interaction. Chaos, Solitons & Fractals, 133, 109614.
  37. Podlubny I. Fractional differential equations. Academic Press, New York; 1999.
  38. Petras I. Fractional -order nonlinear systems: modeling, analysis and simulation. London, Beijing: Springer; 2011.
  39. Özköse, F., Yavuz, M., Şenel, M. T., & Habbireeh, R. (2022). Fractional order modelling of omicron SARS-CoV- 2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons & Fractals, 157,111954.