Araştırma Makalesi

Stochastic Dynamics of Tumor-Immune System

Cilt: 2 Sayı: 1 30 Nisan 2019
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Stochastic Dynamics of Tumor-Immune System

Abstract

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.

Keywords

Kaynakça

  1. J. A. Adam, N. Bellomo, A Survey of Models for Tumor-Immune System Dynamics. Birkh\"{a}user, Boston, MA, 1996.
  2. E. Allen, Modeling with Ito Stochastic Differential Equations, Springer, 2007.
  3. 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.
  4. L. J. S. Allen, An Introduction to Stochastic Processes with Applications to Biology, CRC Press, 2011.
  5. 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.
  6. 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.
  7. 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.
  8. A. Eladdadi, P. Kim, D. Mallet, Mathematical Models of Tumor-Immune System Dynamics, Springer, 2014.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yazarlar

Yayımlanma Tarihi

30 Nisan 2019

Gönderilme Tarihi

19 Aralık 2018

Kabul Tarihi

22 Şubat 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. https://izlik.org/JA74EK49EP
AMA
1.Gökgöz N. Stochastic Dynamics of Tumor-Immune System. RNA. 2019;2(1):1-6. https://izlik.org/JA74EK49EP
Chicago
Gökgöz, Nurgül. 2019. “Stochastic Dynamics of Tumor-Immune System”. Results in Nonlinear Analysis 2 (1): 1-6. https://izlik.org/JA74EK49EP.
EndNote
Gökgöz N (01 Nisan 2019) Stochastic Dynamics of Tumor-Immune System. Results in Nonlinear Analysis 2 1 1–6.
IEEE
[1]N. Gökgöz, “Stochastic Dynamics of Tumor-Immune System”, RNA, c. 2, sy 1, ss. 1–6, Nis. 2019, [çevrimiçi]. Erişim adresi: https://izlik.org/JA74EK49EP
ISNAD
Gökgöz, Nurgül. “Stochastic Dynamics of Tumor-Immune System”. Results in Nonlinear Analysis 2/1 (01 Nisan 2019): 1-6. https://izlik.org/JA74EK49EP.
JAMA
1.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, Nisan 2019, ss. 1-6, https://izlik.org/JA74EK49EP.
Vancouver
1.Nurgül Gökgöz. Stochastic Dynamics of Tumor-Immune System. RNA [Internet]. 01 Nisan 2019;2(1):1-6. Erişim adresi: https://izlik.org/JA74EK49EP