Stochastic modeling of carcinogenesis: State space models and estimation of parameters

Previous Article
Dynamics of a model for brain tumors reveals a small window for therapeutic intervention
DCDS-B Home
This Issue
Next Article
Unraveling the complexity of cell cycle effects of anticancer drugs in cell populations

February 2004, 4(1): 297-322. doi: 10.3934/dcdsb.2004.4.297

Stochastic modeling of carcinogenesis: State space models and estimation of parameters

W. Y. Tan ^1, , L.-J. Zhang ^1, and C.W. Chen ^2,

1.	Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States, United States
2.	United States Environmental Protection Agency (EPA), Washington DC 20460, United States

Received December 2002 Revised September 2003 Published November 2003

Abstract
Related Papers

In this paper we have developed a state space model for carcinogenesis. By using this state space model we have also developed statistical procedures to estimate the unknown parameters via multi-level Gibbs sampling method. We have applied this model and the methods to the British physician data on lung cancer with smoking. Our results indicate that the tobacco nicotine is an initiator. If $t > 60$ years old, then the tobacco nicotine is also a promoter.

Keywords: state space model (Kalman filter model), stochastic differential equations, observation model, stochastic system model., multi-level Gibbs sampling method, MVK two-stage model, Multi-event model of carcinogenesis.

Mathematics Subject Classification: 91B7.

Citation: W. Y. Tan, L.-J. Zhang, C.W. Chen. Stochastic modeling of carcinogenesis: State space models and estimation of parameters. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 297-322. doi: 10.3934/dcdsb.2004.4.297

[1]	Roberta Ghezzi, Benedetto Piccoli. Optimal control of a multi-level dynamic model for biofuel production. Mathematical Control & Related Fields, 2017, 7 (2) : 235-257. doi: 10.3934/mcrf.2017008
[2]	Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667-691. doi: 10.3934/mbe.2018030
[3]	Urszula Foryś, Beata Zduniak. Two-stage model of carcinogenic mutations with the influence of delays. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2501-2519. doi: 10.3934/dcdsb.2014.19.2501
[4]	Dan Liu, Shigui Ruan, Deming Zhu. Stable periodic oscillations in a two-stage cancer model of tumor and immune system interactions. Mathematical Biosciences & Engineering, 2012, 9 (2) : 347-368. doi: 10.3934/mbe.2012.9.347
[5]	G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 517-525. doi: 10.3934/dcdsb.2004.4.517
[6]	Khalid Boushaba. A multi layer method applied to a model of phytoplankton. Networks & Heterogeneous Media, 2007, 2 (1) : 37-54. doi: 10.3934/nhm.2007.2.37
[7]	Biswajit Sarkar, Bijoy Kumar Shaw, Taebok Kim, Mitali Sarkar, Dongmin Shin. An integrated inventory model with variable transportation cost, two-stage inspection, and defective items. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1975-1990. doi: 10.3934/jimo.2017027
[8]	David J. Aldous. A stochastic complex network model. Electronic Research Announcements, 2003, 9: 152-161.
[9]	Pierre Degond, Simone Goettlich, Axel Klar, Mohammed Seaid, Andreas Unterreiter. Derivation of a kinetic model from a stochastic particle system. Kinetic & Related Models, 2008, 1 (4) : 557-572. doi: 10.3934/krm.2008.1.557
[10]	Cécile Appert-Rolland, Pierre Degond, Sébastien Motsch. Two-way multi-lane traffic model for pedestrians in corridors. Networks & Heterogeneous Media, 2011, 6 (3) : 351-381. doi: 10.3934/nhm.2011.6.351
[11]	Miroslava Růžičková, Irada Dzhalladova, Jitka Laitochová, Josef Diblík. Solution to a stochastic pursuit model using moment equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 473-485. doi: 10.3934/dcdsb.2018032
[12]	Graeme Wake, Anthony Pleasants, Alan Beedle, Peter Gluckman. A model for phenotype change in a stochastic framework. Mathematical Biosciences & Engineering, 2010, 7 (3) : 719-728. doi: 10.3934/mbe.2010.7.719
[13]	Lixin Wu, Fan Zhang. LIBOR market model with stochastic volatility. Journal of Industrial & Management Optimization, 2006, 2 (2) : 199-227. doi: 10.3934/jimo.2006.2.199
[14]	TÔn Vı$\underset{.}{\overset{\hat{\ }}{\mathop{\text{E}}}}\, $T T$\mathop {\text{A}}\limits_. $, Linhthi hoai Nguyen, Atsushi Yagi. A sustainability condition for stochastic forest model. Communications on Pure & Applied Analysis, 2017, 16 (2) : 699-718. doi: 10.3934/cpaa.2017034
[15]	Florent Berthelin, Damien Broizat. A model for the evolution of traffic jams in multi-lane. Kinetic & Related Models, 2012, 5 (4) : 697-728. doi: 10.3934/krm.2012.5.697
[16]	Amy Veprauskas, J. M. Cushing. Evolutionary dynamics of a multi-trait semelparous model. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 655-676. doi: 10.3934/dcdsb.2016.21.655
[17]	Eugene Kashdan, Svetlana Bunimovich-Mendrazitsky. Multi-scale model of bladder cancer development. Conference Publications, 2011, 2011 (Special) : 803-812. doi: 10.3934/proc.2011.2011.803
[18]	Shangzhi Li, Shangjiang Guo. Dynamics of a two-species stage-structured model incorporating state-dependent maturation delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1393-1423. doi: 10.3934/dcdsb.2017067
[19]	Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback. Journal of Industrial & Management Optimization, 2008, 4 (1) : 107-123. doi: 10.3934/jimo.2008.4.107
[20]	Liang Zhao. New developments in using stochastic recipe for multi-compartment model: Inter-compartment traveling route, residence time, and exponential convolution expansion. Mathematical Biosciences & Engineering, 2009, 6 (3) : 663-682. doi: 10.3934/mbe.2009.6.663

2018 Impact Factor: 1.008

American Institute of Mathematical Sciences