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Tohidi, Faezeh, Damirchi, Javad, Rezaei, Maryam. (1405). A fractional stochastic differential modeling of cancer cells with an application to the immune response of tumor dynamics. سامانه مدیریت نشریات علمی, 14(3), 1193-1229. doi: 10.22034/cmde.2025.63609.2840
Faezeh Tohidi; Javad Damirchi; Maryam Rezaei. "A fractional stochastic differential modeling of cancer cells with an application to the immune response of tumor dynamics". سامانه مدیریت نشریات علمی, 14, 3, 1405, 1193-1229. doi: 10.22034/cmde.2025.63609.2840
Tohidi, Faezeh, Damirchi, Javad, Rezaei, Maryam. (1405). 'A fractional stochastic differential modeling of cancer cells with an application to the immune response of tumor dynamics', سامانه مدیریت نشریات علمی, 14(3), pp. 1193-1229. doi: 10.22034/cmde.2025.63609.2840
Tohidi, Faezeh, Damirchi, Javad, Rezaei, Maryam. A fractional stochastic differential modeling of cancer cells with an application to the immune response of tumor dynamics. سامانه مدیریت نشریات علمی, 1405; 14(3): 1193-1229. doi: 10.22034/cmde.2025.63609.2840

A fractional stochastic differential modeling of cancer cells with an application to the immune response of tumor dynamics

Computational Methods for Differential Equations
مقاله 13، دوره 14، شماره 3، مهر 2026، صفحه 1193-1229    اصل مقاله (856.09 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.63609.2840
نویسندگان
Faezeh Tohidi1؛ Javad Damirchi* 1؛ Maryam Rezaei2
1Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
2Department of Financial Mathematics, Faculty of Finance Sciences, Kharazmi University, Tehran, Iran.
چکیده
In this paper, we present a fractional stochastic model that examines the response of cancer cells to the immune system. The model combines the long-term memory dependence of fractional derivatives with the stochastic nature of cancer cell growth. The geometric Brownian motion is used to present the stochastic nature of this model. By applying the global derivative from different versions of Caputo-Fabrizio and Atangana-Baleanu fractional derivatives, and converting them into the fractional integral version, we demonstrate the memory property of the model by maintaining the initial conditions. We also prove the stability of the model analytically in the two states of the ordinary differential equation and the fractional differential equation by obtaining the equilibrium points of the model in the disease-free state and the disease state. Additionally, we use the numerical method based on Lagrange polynomials and Newton’s polynomials to examine and compare the approximate solution of the model in two different states: the disease-free state and the disease state. Finally, using numerical simulation, we examine the stability of the model in the fractional-random state. We show that using Newton’s polynomial will preserve the stability condition better than Lagrange’s polynomial. Further, we demonstrate that the solutions of the stochastic fractional model are positive and bounded, and we also prove their uniqueness and existence.
کلیدواژه‌ها
Cancer model؛ Immune system؛ Fractional stochastic differential equations؛ fractional derivatives؛ Numerical approximations
مراجع
  • [1] B. S. T. Alkahtani and I. Koca, Fractional stochastic sır model, Results in Physics, 24 (2021), 104124.
  • [2] A. Atangana and Si. Araz, Atangana–Seda numerical scheme for Labyrinth attractor with new differential and integral operators, Fractals, 28(08) (2020), 2040044.
  • [3] A. Atangana and Si. Araz, New numerical scheme with Newton polynomial: theory, methods, and applications, Academic Press, 2021.
  • [4] A. Atangana and Si. Araz, Nonlinear equations with global differential and integral operators: existence, uniqueness with application to epidemiology, Results in Physics, 20 (2021), 103593.
  • [5] A. Atangana and Si. Araz, Extension of successive midpoint scheme for nonlinear differential equations with global nonlocal operators, Alexandria Engineering Journal, 111 (2025), 374–384.
  • [6] A. Atangana, Modelling the spread of COVID-19 with new fractal-fractional operators: can the lockdown save mankind before vaccination?, Chaos, Solitons & Fractals, 136 (2020), 109860.
  • [7] A. Atangana, Extension of rate of change concept: from local to nonlocal operators with applications, Results in Physics, 19 (2020), 103515.
  • [8] S. K. Choi, B. Kang, and N. Koo, Stability for Caputo fractional differential systems, Abstract and Applied Analysis, 2014(1) (2014), 631419.
  • [9] J. J. Crivelli, J. Földes, P. S. Kim, and J. R. A. Wares, A mathematical model for cell cycle-specific cancer virotherapy, Journal of Biological Dynamics, 6(sup1) (2012), 104–120.
  • [10] M. H. DarAssi, I. Ahmad, M. Z. Meetei, M. Alsulami, M. A. Khan, and E. M. Tag-eldin, The impact of the face mask on SARS-CoV-2 disease: Mathematical modeling with a case study, Results in Physics, 51 (2023), 106699.
  • [11] J. D. Djida, I. Area, and A. Atangana, New numerical scheme of Atangana-Baleanu fractional integral: an application to groundwater flow within leaky aquifer, arXiv preprint arXiv:1610.08681, (2016).
  • [12] A. M. Elaiw and A. D. Al Agha, Analysis of a delayed and diffusive oncolytic M1 virotherapy model with immune response, Nonlinear Analysis: Real World Applications, 55 (2020), 103116.
  • [13] F. Guo, W. Zhou, Q. Lu, and C. Zhang, Path extension similarity link prediction method based on matrix algebra in directed networks, Computer Communications, 187 (2022), 83–92.
  • [14] H. Y. Jin and Z. A. Wang, Global stabilization of the full attraction-repulsion Keller-Segel system, arXiv preprint arXiv:1905.05990, (2019).
  • [15] S. Li, I. Bukhsh, I. U. Khan, M. I. Asjad, S. M. Eldin, M. A. El-Rahman, and D. Baleanu, The impact of standard and nonstandard finite difference schemes on HIV nonlinear dynamical model, Chaos, Solitons & Fractals, 173 (2023), 113755.
  • [16] P. Liu, J. Shi, and Z. A. Wang, Pattern formation of the attraction-repulsion Keller-Segel system, Discrete Contin. Dyn. Syst. Ser. B, 18(10) (2013), 2597–2625.
  • [17] A. Nouni, K. Hattaf, and N. Yousfi, Dynamics of a Virological Model for Cancer Therapy with Innate Immune Response, Complexity, 2020(1) (2020), 8694821.
  • [18] R. B. Nussenblatt and K. Csaky, Perspectives on gene therapy in the treatment of ocular inflammation, Eye, 11(2) (1997), 217–221.
  • [19] M. Partohaghighi, M. S. Hashemi, M. Mirzazadeh, and S. M. El Din, Numerical method for fractional Advection– Dispersion equation using shifted Vieta–Lucas polynomials, Results in Physics, 52 (2023), 106756.
  • [20] A. Raza, J. Awrejcewicz, M. Rafiq, N. Ahmed, and M. Mohsin, Stochastic analysis of nonlinear cancer disease model through virotherapy and computational methods, Mathematics, 10(3) (2022), 368.
  • [21] A. Selvam, S. Sabarinathan, B. V. Senthil Kumar, H. Byeon, K. Guedri, S. M. Eldin, M. L. Khan, and V. Govin- dan, Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal- fractional operator, Scientific Reports, 13(1) (2023), 9012.
  • [22] L. W. Seymour and K. D. Fisher, Oncolytic viruses: finally delivering, British Journal of Cancer, 114(4) (2016), 357–361.
  • [23] M. Toufik and A. Atangana, New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models, The European Physical Journal Plus, 132 (2017), 1–16.
  • [24] E. U¸car and N. Özdemir, A fractional model of cancer-immune system with Caputo and Caputo–Fabrizio derivatives, The European Physical Journal Plus, 136(1) (2021), 43.
  • [25] Z. U. A. Zafar, M. H. DarAssi, I. Ahmad, T. A. Assiri, M. Z. Meetei, M. A. Khan, and A. M. Hassan, Numerical simulation and analysis of the stochastic HIV/AIDS model in fractional order, Results in Physics, 53 (2023), 106995.
  • [26] M. Zheng, J. Huang, A. Tong, and H. Yang, Oncolytic viruses for cancer therapy: barriers and recent advances, Molecular Therapy-Oncolytics, 15 (2019), 234–247.
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