Cancer modelling
Open Access
Math. Model. Nat. Phenom.
Volume 16, 2021
Cancer modelling
Article Number 14
Number of page(s) 21
Published online 22 March 2021
  1. J. Adam and J.C. Panetta, A simple mathematical model and alternative paradigm for certain chemotherapeutic regimens. Mats. Comput. Model. 22 (1995) 49–60. [Google Scholar]
  2. E. Ahmed, A.H. Hashis and F.A. Rihan, On fractional order cancer model. J. fract. Calc. Appl. 3 (2012) 1–6. [Google Scholar]
  3. I.A. Baba, A fractional-order bladder cancermodel with BCG treatment effect. Comput. Appl. Math. 38 (2019) 37. [Google Scholar]
  4. D. Baleanu, A. Jajarmi, S.S. Sajjadi and D. Mozyrska, A new fractional model and optimal control of a tumor-immune surveillance with nonsingular derivative operator. Chaos 29 (2019) 083127. [Google Scholar]
  5. D. Baleanu, Z.B. Güvenç and J.T. Machado, New Trends in Nanotechnology and Fractional Calculus Applications. Springer (2010). [Google Scholar]
  6. M. Cai and C. Li, Numerical approaches to fractional integrals and derivatives: a review. Mathematics 8 (2020) 43. [Google Scholar]
  7. M. Caputo, Elasticita e Dissipazione, Zanichelli, CityplaceBologna (1965). [Google Scholar]
  8. O. Defterli, Modeling the impact of temperature on fractional order dengue model with vertical transmission. Int. J. Optim. Control: Theories Appl. 1 (2020) 85–93. [Google Scholar]
  9. K. Diethelm, The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo type, Lecture Notes in Mathematics nr. 2004, Springer, Heidelbereg (2010). [Google Scholar]
  10. D. Dingli, M.D. Cascino, K. Josic, S.J. Russell and Z. Bajzer, Mathematical modeling of cancer radiovirotherapy. Math Biosci. 199 (2006) 55–78. [Google Scholar]
  11. G. Ertas, Fitting intravoxel incoherent motion model to diffusion MR signals of the human breast tissue using particle swarm optimization. Int. J. Optim. Control: Theories Appl. 2 (2019) 105–112. [Google Scholar]
  12. F. Evirgen, S. Ucar and N. Ozdemir, Analysis of HIV infection model with CD4+Tunder non-singular kernel derivative. Appl. Math. Nonlinear Sci. 5 (2020) 139–146. [Google Scholar]
  13. R. Garrappa, E. Kaslik and M. Popolizio, Evaluation of fractional integrals and derivatives of elementary functions: overview and tutorial. Mathematics 7 (2019) 407. [Google Scholar]
  14. A. Giusti and I. Colombaro, Prabhakar-like fractional viscoelasticity. Commun. Nonlinear Sci. Numer. Simulat. 56 (2018) 138–143. [Google Scholar]
  15. R. Hilfer and Y. Luchko, Desiderata for fractional derivatives and integrals. Mathematics 7 (2019) 149. [Google Scholar]
  16. J. Hristov, Linear viscoelastic responses and constitutive equations in terms of fractional operators with non-singular kernels. Pragmatic approach, memory kernel correspondence requirement and analyses. Eur. Phys. J. Plus 134 (2019) 283. [Google Scholar]
  17. O.G. Isaeva and V.A. Osipov, Different strategies for cancer treatment: mathematical modeling. Comput. Math. Methods Med. 10 (2009) 453–72. [Google Scholar]
  18. O.S. Iyiola and F.D. Zaman, A fractional diffusion equation model for cancer tumor. AIP Adv. 4 (2014) 107121. [Google Scholar]
  19. Z. Ji, K. Yan, W. Li, H. Hu and X. Zhu, Mathematical and computational modeling in complex biological systems. BioMed Res. Int. 2017 (2017) 5958321. [Google Scholar]
  20. M.A. Khan, M. Parvez, S. Islam, I. Khan, S. Shafie and T. Gul, Mathematical analysis of typhoid model with saturated incidencerate. Adv. Stud. Biol. 7 (2015) 65–78. [Google Scholar]
  21. I. Koka, Analysis of rubella disease model with non-local and non-singular fractional derivatives. Int. J. Optim. Control: Theories Appl. 1 (2018) 17–25. [Google Scholar]
  22. A. Kremling, Systems Biology: Mathematical Modeling and Model Analysis. Mathematical and Computational Biology Series. Chapman & Hall/CRC Boca Raton, USA (2014). [Google Scholar]
  23. H. Li, J. Cao and C. Li, High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (III), J. Comput. Appl. Math. 299 (2016) 159–175. [Google Scholar]
  24. W. Liu, T. Hillen and H.I. Freedman, A mathematical model for M-phase specific chemotherapy including the G0-phase and immunoresponse. Math. Biosci. Eng. 4 (2007) 239–259. [PubMed] [Google Scholar]
  25. Z. Liu and C. Yang, A mathematical model of cancer treatment by radiotherapy. Comput. Math. Methods Med. 2014 (2014) 172923. [PubMed] [Google Scholar]
  26. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College Press (2010). [Google Scholar]
  27. J. Manimaran, L. Shangerganesh, A. Debbouche and V. Antonov, Numerical solutions for time-fractional cancer invasion system with nonlocal diffusion. Front Phys. 7 (2019) 93. [Google Scholar]
  28. P.A. Naik, K.M. Owolabi, M. Yavuz and J. Zu, Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells. Chaos Solitons Fract. 140 (2020) 110272. [Google Scholar]
  29. N. Özdemir, S. Uçar and B.B.I. Eroglu, Dynamical analysis of fractional order model for computer virus propagation with kill signals. IJNSNS 21 (2020) 239–247. [Google Scholar]
  30. J.C. Panetta and J. Adam, A mathematical model of cycle-specific chemotherapy. Math. Comput. Model. 22 (1995) 67–82. [Google Scholar]
  31. J.C. Panetta, A mathematical model of breast and ovarian cancer treated with Paclitaxel. Math. Biosci. 146 (1997) 89–113. [Google Scholar]
  32. J.E. Solis-Perez, J.F. Gomez-Aguilar and A. Atangana, A fractional mathematical model of breast cancer competition model. Chaos Solitons Fract. 127 (2019) 38–54. [Google Scholar]
  33. V.E. Tarasov and G.M. Zaslavsky, Fractional dynamics of systems with long-range interaction. Commun. Nonlinear Sci. Numer. Simulat. 11 (2006) 885–898. [Google Scholar]
  34. J.A. Tuszynski, P. Winter, D. White, C.Y. Tseng, K.K. Sahu, F. Gentile, I. Spasevska, S.I. Omar, N. Nayebi, C.D.M. Churchill, M. Klobukowski and R.M. Abou El-Magd, Mathematical and computational modeling in biology at multiple scales. Theor. Biol. Med. Model. 11 (2014) 52. [PubMed] [Google Scholar]
  35. E. Ucar, N.Ozdemir and E. Altun, Fractional order model of immune cells influenced by cancer cells. MMNP 14 (2019) 308. [EDP Sciences] [Google Scholar]
  36. S. Ucar, E. Ucar, N. Ozdemir and Z. Hammouch, Mathematical analysis and numerical simulation for a smoking model with Atangana-Baleanu derivative. Chaos Solitons Fractals 118 (2019) 300–308. [Google Scholar]
  37. P. Unni and P. Seshaiyer, Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions. Comput. Math. Methods Med. 2019 (2019) 4079298. [PubMed] [Google Scholar]
  38. J.R. Usher, Some mathematical models for cancer chemotherapy. Comput. Math. Appl. 28 (1994) 73–80. [Google Scholar]
  39. S. Wang and H. Schattler, Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Math. BioSciences 13 (2016) 1223–1240. [Google Scholar]
  40. G.F. Webb, A nonlinear cell population model of periodic chemotherapy treatment. Vol. I of Recent Trends in Ordinary Differential Equations. Series in Applicable Analysis. World Scientific (1992) 569–583. [Google Scholar]
  41. H.N. Weerasinghe, P.M. Burrage, K. Burrage and D.V. Nicolau Jr., Mathematical models of cancer cell plasticity. J. Oncol. 2019 (2019) 2403483. [Google Scholar]
  42. M. Yavuz and N. Ozdemir, Analysis of an epidemic spreading model with exponential decay law. Math. Sci. Appl. E-Notes 1 (2020) 142–154. [Google Scholar]
  43. M. Yavuzand N. Sene, Stability analysis and numerical computation of the fractional predator-prey model with the harvesting rate. Fractal Fract. 4 (2020) 35. [Google Scholar]
  44. A. Yin, D.J.A.R. Moes, J.G.C. van Hasselt, J.J. Swen and H.J. Guchelaar, A review of mathematical models for tumor dynamicsand treatment resistance evolution of solid tumors. CPT Pharmacometrics Syst. Pharmacol. 8 (2019) 720–737. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.