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Year 2025, Volume: 8 Issue: 2, 86 - 92, 28.06.2025
https://doi.org/10.33187/jmsm.1681375

Abstract

References

  • [1] V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor, et al., Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bull. Math. Biol., 56(2) (1994), 295–321. http://dx.doi.org/10.1007/BF02460644
  • [2] L. G. de Pillis, W. Gu, A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations, J. Theoret. Biol., 238(4) (2006), 841–862. https://doi.org/10.1016/j.jtbi.2005.06.037
  • [3] L. G. De Pillis, A. Radunskaya, The dynamics of an optimally controlled tumor model: A case study, Math. Comput. Modelling, 37(11) (2003), 1221–1244. https://doi.org/10.1016/S0895-7177(03)00133-X
  • [4] A. d’Onofrio, A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D: Nonlinear Phenom., 208(3-4) (2005), 220–235. https://doi.org/10.1016/j.physd.2005.06.032
  • [5] D. Kirschner, J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235–252. https://doi.org/10.1007/s002850050127
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  • [21] I. Bashkirtseva, L. Ryashko, A. G. L´opez, et al., The effect of time ordering and concurrency in a mathematical model of chemoradiotherapy, Commun. Nonlinear Sci. Numer. Simul., 96 (2021), Article ID 105693. https://doi.org/10.1016/j.cnsns.2021.105693
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  • [24] M. Sardar, S. Khajanchi, S. Biswas, Stochastic dynamics of a nonlinear tumor-immune competitive system, Nonlinear Dyn., 113 (2025), 4395-4423. https://doi.org/10.1007/s11071-024-09768-5
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  • [26] M. Sardar, S. Khajanchi, Is the Allee effect relevant to stochastic cancer model?, J. Appl. Math. Comput., 68 (2022), 2293-2315. https://doi.org/10.1007/s12190-021-01618-6
  • [27] S. Khajanchi, J. J. Nieto, Spatiotemporal dynamics of a glioma immune interaction model, Sci. Rep., 11 (2021), Article ID 22385. https://doi.org/10.1038/s41598-021-00985-1
  • [28] S. Khajanchi, The impact of immunotherapy on a glioma immune interaction model, Chaos Solitons Fractals, 152 (2021), Article ID 111346. https://doi.org/10.1016/j.chaos.2021.111346
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  • [35] S. Abernethy, R. J. Gooding, The importance of chaotic attractors in modelling tumour growth, Phys. A: Stat. Mech. Appl., 507 (2018), 268–277. https://doi.org/10.1016/j.physa.2018.05.093
  • [36] S. Yılmaz, Stabilization of chaos in a cancer model: The effect of oncotripsy, Balkan J. Electr. Comput. Eng., 10(2) (2022), 139–149. https://doi.org/10.17694/bajece.1039384
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Tumor–Immune Dynamics: A Spatial-Spectral Perspective

Year 2025, Volume: 8 Issue: 2, 86 - 92, 28.06.2025
https://doi.org/10.33187/jmsm.1681375

Abstract

Mathematical modeling of tumor–immune interactions provides valuable insights into the nonlinear dynamics that govern tumor progression and response to treatment. In this study, a deterministic model of the tumor–immune system under chemotherapy is investigated with a focus on spectral entropy and basin of attraction analyses. Spectral entropy is applied to quantify the temporal complexity of system dynamics and to detect transitions between qualitatively distinct behavioral regimes, such as steady states, oscillatory patterns, and potentially chaotic trajectories. Basin of attraction analysis investigates how variations in the initial populations of tumor and immune cells determine the long-term behavior of the system, including tumor elimination, persistent oscillations, or uncontrolled tumor growth. By combining spectral entropy with basin mapping, the framework captures both the temporal irregularity and the sensitivity to initial conditions inherent in tumor–immune dynamics, which may help guide the design and timing of more effective therapeutic interventions.

References

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  • [3] L. G. De Pillis, A. Radunskaya, The dynamics of an optimally controlled tumor model: A case study, Math. Comput. Modelling, 37(11) (2003), 1221–1244. https://doi.org/10.1016/S0895-7177(03)00133-X
  • [4] A. d’Onofrio, A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D: Nonlinear Phenom., 208(3-4) (2005), 220–235. https://doi.org/10.1016/j.physd.2005.06.032
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  • [6] V. A. Kuznetsov, G. D. Knott, Modeling tumor regrowth and immunotherapy, Math. Comput. Modelling, 33(12-13) (2001), 1275–1287. https://doi.org/10.1016/S0895-7177(00)00314-9
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  • [12] S. Khajanchi, M. Perc, D. Ghosh, The influence of time delay in a chaotic cancer model, Chaos, 28(10) (2018), Article ID 103101. https://doi.org/10.1063/1.5052496
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  • [19] S. Khajanchi, J. Mondal, P. K. Tiwari, Optimal treatment strategies using dendritic cell vaccination for a tumor model with parameter identifiability, J. Biol. Syst., 31(02) (2023), 487-516. https://doi.org/10.1142/S0218339023500171
  • [20] I. Bashkirtseva, A. Chukhareva, L. Ryashko, Modeling and analysis of nonlinear tumor-immune interaction under chemotherapy and radiotherapy, Math. Methods Appl. Sci., 45(13) (2022), 7983–7991. https://doi.org/10.1002/mma.7706
  • [21] I. Bashkirtseva, L. Ryashko, A. G. L´opez, et al., The effect of time ordering and concurrency in a mathematical model of chemoradiotherapy, Commun. Nonlinear Sci. Numer. Simul., 96 (2021), Article ID 105693. https://doi.org/10.1016/j.cnsns.2021.105693
  • [22] I. Bashkirtseva, L. Ryashko, J. M. Seoane, et al., Chaotic transitions in a tumor-immune model under chemotherapy treatment, Commun. Nonlinear Sci. Numer. Simul., 132 (2024), Article ID 107946. https://doi.org/10.1016/j.cnsns.2024.107946
  • [23] G. Torres Espino, C. Vidal, Dynamics aspects and bifurcations of a tumor-immune system interaction under stationary immunotherapy, Math. Biosci., 369 (2024), Article ID 109145. https://doi.org/10.1016/j.mbs.2024.109145
  • [24] M. Sardar, S. Khajanchi, S. Biswas, Stochastic dynamics of a nonlinear tumor-immune competitive system, Nonlinear Dyn., 113 (2025), 4395-4423. https://doi.org/10.1007/s11071-024-09768-5
  • [25] S. Khajanchi, M. Sardar, J. J. Nieto, Application of non-singular kernel in a tumor model with strong Allee effect, Differ. Equ. Dyn. Syst., 31(3) (2023), 687-692. https://doi.org/10.1007/s12591-022-00622-x
  • [26] M. Sardar, S. Khajanchi, Is the Allee effect relevant to stochastic cancer model?, J. Appl. Math. Comput., 68 (2022), 2293-2315. https://doi.org/10.1007/s12190-021-01618-6
  • [27] S. Khajanchi, J. J. Nieto, Spatiotemporal dynamics of a glioma immune interaction model, Sci. Rep., 11 (2021), Article ID 22385. https://doi.org/10.1038/s41598-021-00985-1
  • [28] S. Khajanchi, The impact of immunotherapy on a glioma immune interaction model, Chaos Solitons Fractals, 152 (2021), Article ID 111346. https://doi.org/10.1016/j.chaos.2021.111346
  • [29] S. Sabarathinam, K. Thamilmaran, Controlling of chaos in a tumour growth cancer model: An experimental study, Electron. Lett., 54(20) (2018), 1160–1162. https://doi.org/10.1049/el.2018.5126
  • [30] M. Saleem, M. Y. Baba, A. Raheem, et al., A caution for oncologists: Chemotherapy can cause chaotic dynamics, Comput. Methods Programs Biomed., 200 (2021), Article ID 105865. https://doi.org/10.1016/j.cmpb.2020.105865
  • [31] I. Bashkirtseva, A. Chukhareva, L. Ryashko, Stochastic dynamics of nonlinear tumor–immune system with chemotherapy, Phys. A: Stat. Mech. Appl., 622 (2023), Article ID 128835. https://doi.org/10.1016/j.physa.2023.128835
  • [32] I. Bashkirtseva, L. Ryashko, Analysis of noise-induced phenomena in the nonlinear tumor–immune system, Phys. A, 549 (2020), Article ID 123923. https://doi.org/10.1016/j.physa.2019.123923
  • [33] I. Bashkirtseva, L. Ryashko, J. Duarte, et al., The role of noise in the tumor dynamics under chemotherapy treatment, Eur. Phys. J. Plus, 136 (2021), 1–13, Article ID 1123. https://doi.org/10.1140/epjp/s13360-021-02061-z
  • [34] X. Liu, Q. Li, J. Pan, A deterministic and stochastic model for the system dynamics of tumor-immune responses to chemotherapy, Phys. A: Stat. Mech. Appl., 500 (2018), 162–176. https://doi.org/10.1016/j.physa.2018.02.118
  • [35] S. Abernethy, R. J. Gooding, The importance of chaotic attractors in modelling tumour growth, Phys. A: Stat. Mech. Appl., 507 (2018), 268–277. https://doi.org/10.1016/j.physa.2018.05.093
  • [36] S. Yılmaz, Stabilization of chaos in a cancer model: The effect of oncotripsy, Balkan J. Electr. Comput. Eng., 10(2) (2022), 139–149. https://doi.org/10.17694/bajece.1039384
  • [37] G. Powell, I. Percival, A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems, J. Phys. A: Math. Gen., 12(11) (1979), Article ID 2053. https://doi.org/10.1088/0305-4470/12/11/017
  • [38] H. Helakari, J. Kananen, N. Huotari, et.al, Spectral entropy indicates electrophysiological and hemodynamic changes in epilepsy, NeuroImage Clin., 22 (2019), Article ID 101763. https://doi.org/10.1016/j.nicl.2019.101763
  • [39] F. Luque-Su´arez, A. Camarena-Ibarrola, E. Ch´avez, Efficient speaker identification using spectral entropy, Multimed. Tools Appl., 78 (2019), 16803-16815. https://doi.org/10.1007/s11042-018-7035-9
  • [40] A. M. Toh, R. Togneri, S. Nordholm, Spectral entropy as speech features for speech recognition, Proc. PEECS, 1 (2005), Article ID 92.
  • [41] H. Misra, S. Ikbal, H. Bourlard, et al., Spectral entropy based feature for robust ASR, Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 1 (2004), 1–193. https://doi.org/10.1109/ICASSP.2004.1325955
  • [42] K. Wang, Z. J. Xu, Y. Gong, et al., Mechanical fault prognosis through spectral analysis of vibration signals, Algorithms, 15(3) (2022), Article ID 94. https://doi.org/10.3390/a15030094
  • [43] G. Datseris, A. Wagemakers, Effortless estimation of basins of attraction, Chaos, 32(2) (2022), Article ID 023104. https://doi.org/10.1063/5.0076568
There are 43 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Serpil Yılmaz 0000-0002-6276-6058

Early Pub Date June 25, 2025
Publication Date June 28, 2025
Submission Date April 21, 2025
Acceptance Date June 24, 2025
Published in Issue Year 2025 Volume: 8 Issue: 2

Cite

APA Yılmaz, S. (2025). Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling, 8(2), 86-92. https://doi.org/10.33187/jmsm.1681375
AMA Yılmaz S. Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling. June 2025;8(2):86-92. doi:10.33187/jmsm.1681375
Chicago Yılmaz, Serpil. “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”. Journal of Mathematical Sciences and Modelling 8, no. 2 (June 2025): 86-92. https://doi.org/10.33187/jmsm.1681375.
EndNote Yılmaz S (June 1, 2025) Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling 8 2 86–92.
IEEE S. Yılmaz, “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, pp. 86–92, 2025, doi: 10.33187/jmsm.1681375.
ISNAD Yılmaz, Serpil. “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”. Journal of Mathematical Sciences and Modelling 8/2 (June 2025), 86-92. https://doi.org/10.33187/jmsm.1681375.
JAMA Yılmaz S. Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling. 2025;8:86–92.
MLA Yılmaz, Serpil. “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, 2025, pp. 86-92, doi:10.33187/jmsm.1681375.
Vancouver Yılmaz S. Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling. 2025;8(2):86-92.

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