American Institute of Mathematical Sciences

Advanced
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

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 and 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 and Related Fields, 2017, 7 (2) : 235-257. doi: 10.3934/mcrf.2017008
[2]

Li Deng, Wenjie Bi, Haiying Liu, Kok Lay Teo. A multi-stage method for joint pricing and inventory model with promotion constrains. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1653-1682. doi: 10.3934/dcdss.2020097
[3]

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
[4]

Zhimin Liu, Shaojian Qu, Hassan Raza, Zhong Wu, Deqiang Qu, Jianhui Du. Two-stage mean-risk stochastic mixed integer optimization model for location-allocation problems under uncertain environment. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2783-2804. doi: 10.3934/jimo.2020094
[5]

Urszula Foryś, Beata Zduniak. Two-stage model of carcinogenic mutations with the influence of delays. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2501-2519. doi: 10.3934/dcdsb.2014.19.2501
[6]

Sun-Ho Choi, Hyowon Seo, Minha Yoo. A multi-stage SIR model for rumor spreading. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2351-2372. doi: 10.3934/dcdsb.2020124
[7]

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
[8]

G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 517-525. doi: 10.3934/dcdsb.2004.4.517
[9]

Dimitra C. Antonopoulou, Marina Bitsaki, Georgia Karali. The multi-dimensional stochastic Stefan financial model for a portfolio of assets. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1955-1987. doi: 10.3934/dcdsb.2021118
[10]

Khalid Boushaba. A multi layer method applied to a model of phytoplankton. Networks and Heterogeneous Media, 2007, 2 (1) : 37-54. doi: 10.3934/nhm.2007.2.37
[11]

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 and Management Optimization, 2017, 13 (4) : 1975-1990. doi: 10.3934/jimo.2017027
[12]

David J. Aldous. A stochastic complex network model. Electronic Research Announcements, 2003, 9: 152-161.

[13]

Miljana Jovanović, Vuk Vujović. Stability of stochastic heroin model with two distributed delays. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2407-2432. doi: 10.3934/dcdsb.2020016
[14]

Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. A stage structured model of delay differential equations for Aedes mosquito population suppression. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3467-3484. doi: 10.3934/dcds.2020042
[15]

Pierre Degond, Simone Goettlich, Axel Klar, Mohammed Seaid, Andreas Unterreiter. Derivation of a kinetic model from a stochastic particle system. Kinetic and Related Models, 2008, 1 (4) : 557-572. doi: 10.3934/krm.2008.1.557
[16]

Caterina Balzotti, Simone Göttlich. A two-dimensional multi-class traffic flow model. Networks and Heterogeneous Media, 2021, 16 (1) : 69-90. doi: 10.3934/nhm.2020034
[17]

Cécile Appert-Rolland, Pierre Degond, Sébastien Motsch. Two-way multi-lane traffic model for pedestrians in corridors. Networks and Heterogeneous Media, 2011, 6 (3) : 351-381. doi: 10.3934/nhm.2011.6.351
[18]

Miroslava Růžičková, Irada Dzhalladova, Jitka Laitochová, Josef Diblík. Solution to a stochastic pursuit model using moment equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 473-485. doi: 10.3934/dcdsb.2018032
[19]

Seung-Yeal Ha, Dohyun Kim, Jaeseung Lee, Se Eun Noh. Emergent dynamics of an orientation flocking model for multi-agent system. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2037-2060. doi: 10.3934/dcds.2020105
[20]

Mojtaba F. Fathi, Ahmadreza Baghaie, Ali Bakhshinejad, Raphael H. Sacho, Roshan M. D'Souza. Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother. Journal of Computational Dynamics, 2020, 7 (2) : 469-487. doi: 10.3934/jcd.2020019

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (104)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy