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Stochastic Dynamics of Tumor-Immune System

Yıl 2019, Cilt: 2 Sayı: 1, 1 - 6, 30.04.2019

Öz

In this work, a very well known tumor-immune system model from the literature, Kuznetsov et al.'s model, is converted into two different Stochastic Differential Equation (SDE) models and an It\^{o} formalism of the models are obtained. Furthermore, the models are made discrete by using Euler-Maruyama scheme, simulation results of the corresponding models are investigated and compared.

Kaynakça

  • J. A. Adam, N. Bellomo, A Survey of Models for Tumor-Immune System Dynamics. Birkh\"{a}user, Boston, MA, 1996.
  • E. Allen, Modeling with Ito Stochastic Differential Equations, Springer, 2007.
  • E. J. Allen, L. J. S. Allen, A. Arciniega, P. Greenwood, Construction of equivalent stochastic differential equation models. Stoch. Anal. Appl., 26, pages: 274-297, 2008.
  • L. J. S. Allen, An Introduction to Stochastic Processes with Applications to Biology, CRC Press, 2011.
  • J. C. Arciero, T. L. Jackson, D. Kirschner, A Mathematical Model of Tumor-Immune Evasion and siRNA Treatment, Discrete and Continuous Dynamical Systems- Series B, Volume 4, Number 1, Pages:39-58, 2004.
  • N. Bellomo, M. Delitala, From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells, Physics of Life Reviews, Volume 5, Issue 4, Pages 183-206, December 2008.
  • J. Cresson, S. Sonner, A note on a derivation method for SDE models: Application in biology and viability criteria, Stochastic Analysis and Applications, Vol. 36, No. 2, pages 224-239, 2018.
  • A. Eladdadi, P. Kim, D. Mallet, Mathematical Models of Tumor-Immune System Dynamics, Springer, 2014.
  • R. A. Gatenby, T. L. Vincent, Application of quantitative models from population biology andevolutionary game theory to tumor therapeutic strategies, Mol Cancer Ther., 2(9):919-27, 2003.
  • D. Kirschner, J.C. Panetta. Modeling immunotherapy of the tumor-immune interaction. J Math Biol., 37(3):235-52, 1998.
  • V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor, A. S. Perelson. Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcations analysis. Bull Math Biol., 56(2):295-321, 1994.
  • D. G. Mallet, L. G. De Pillis, A cellular automata model of tumor–immune system interactions, Journal of Theoretical Biology, Volume 239, Issue 3, Pages 334-350, 2006.
  • L. G. de Pillis, A. E. Radunskaya, C. L. Wiseman, A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth, Cancer Res., 65(17):7950-8, 2005.
  • M. Robertson-Tessi, A. El-Kareh, A. Goriely. A mathematical model of tumor-immune interactions. J Theor Biol., 294:56-73, 2012.
Yıl 2019, Cilt: 2 Sayı: 1, 1 - 6, 30.04.2019

Öz

Kaynakça

  • J. A. Adam, N. Bellomo, A Survey of Models for Tumor-Immune System Dynamics. Birkh\"{a}user, Boston, MA, 1996.
  • E. Allen, Modeling with Ito Stochastic Differential Equations, Springer, 2007.
  • E. J. Allen, L. J. S. Allen, A. Arciniega, P. Greenwood, Construction of equivalent stochastic differential equation models. Stoch. Anal. Appl., 26, pages: 274-297, 2008.
  • L. J. S. Allen, An Introduction to Stochastic Processes with Applications to Biology, CRC Press, 2011.
  • J. C. Arciero, T. L. Jackson, D. Kirschner, A Mathematical Model of Tumor-Immune Evasion and siRNA Treatment, Discrete and Continuous Dynamical Systems- Series B, Volume 4, Number 1, Pages:39-58, 2004.
  • N. Bellomo, M. Delitala, From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells, Physics of Life Reviews, Volume 5, Issue 4, Pages 183-206, December 2008.
  • J. Cresson, S. Sonner, A note on a derivation method for SDE models: Application in biology and viability criteria, Stochastic Analysis and Applications, Vol. 36, No. 2, pages 224-239, 2018.
  • A. Eladdadi, P. Kim, D. Mallet, Mathematical Models of Tumor-Immune System Dynamics, Springer, 2014.
  • R. A. Gatenby, T. L. Vincent, Application of quantitative models from population biology andevolutionary game theory to tumor therapeutic strategies, Mol Cancer Ther., 2(9):919-27, 2003.
  • D. Kirschner, J.C. Panetta. Modeling immunotherapy of the tumor-immune interaction. J Math Biol., 37(3):235-52, 1998.
  • V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor, A. S. Perelson. Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcations analysis. Bull Math Biol., 56(2):295-321, 1994.
  • D. G. Mallet, L. G. De Pillis, A cellular automata model of tumor–immune system interactions, Journal of Theoretical Biology, Volume 239, Issue 3, Pages 334-350, 2006.
  • L. G. de Pillis, A. E. Radunskaya, C. L. Wiseman, A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth, Cancer Res., 65(17):7950-8, 2005.
  • M. Robertson-Tessi, A. El-Kareh, A. Goriely. A mathematical model of tumor-immune interactions. J Theor Biol., 294:56-73, 2012.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Nurgül Gökgöz

Yayımlanma Tarihi 30 Nisan 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 1

Kaynak Göster

APA Gökgöz, N. (2019). Stochastic Dynamics of Tumor-Immune System. Results in Nonlinear Analysis, 2(1), 1-6.
AMA Gökgöz N. Stochastic Dynamics of Tumor-Immune System. RNA. Nisan 2019;2(1):1-6.
Chicago Gökgöz, Nurgül. “Stochastic Dynamics of Tumor-Immune System”. Results in Nonlinear Analysis 2, sy. 1 (Nisan 2019): 1-6.
EndNote Gökgöz N (01 Nisan 2019) Stochastic Dynamics of Tumor-Immune System. Results in Nonlinear Analysis 2 1 1–6.
IEEE N. Gökgöz, “Stochastic Dynamics of Tumor-Immune System”, RNA, c. 2, sy. 1, ss. 1–6, 2019.
ISNAD Gökgöz, Nurgül. “Stochastic Dynamics of Tumor-Immune System”. Results in Nonlinear Analysis 2/1 (Nisan 2019), 1-6.
JAMA Gökgöz N. Stochastic Dynamics of Tumor-Immune System. RNA. 2019;2:1–6.
MLA Gökgöz, Nurgül. “Stochastic Dynamics of Tumor-Immune System”. Results in Nonlinear Analysis, c. 2, sy. 1, 2019, ss. 1-6.
Vancouver Gökgöz N. Stochastic Dynamics of Tumor-Immune System. RNA. 2019;2(1):1-6.