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A Stochastic Growth Model for Cancer Cells under Mutation and Metastasis in an Organ

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This study has proposed a stochastic model for cancerous growth due to its metastasis in an organ. The birth-and-death and migration processes based on growth and loss rates of pathogenesis of malignant and normal cells are considered. It is assumed that the growth and loss/death rates of both normal and malignant cells follows Poisson processes. The joint probability generating functions in the form of partial differential equation along with statistical measures were derived in terms of system of ordinary differential equations. The Model behaviour was analysed by solving those differential equations and presented graphically.


International Frontier Science Letters (Volume 8)
J. Jayabharathiraj "A Stochastic Growth Model for Cancer Cells under Mutation and Metastasis in an Organ", International Frontier Science Letters, Vol. 8, pp. 19-30, 2016
Online since:
Jun 2016

[1] G. Serio, Two-Stage Stochastic Model for Carcinogenesis with Time-Dependent Parameters, Statistics & Probability Letters 2(1984) 95-103.

DOI: 10.1016/0167-7152(84)90057-9

[2] W. Y. Tan, A stochastic model for the formation of metastatic foci at distant sites. Mathematical and Computer Modelling. 12(1989) 1093–1102.

DOI: 10.1016/0895-7177(89)90230-6

[3] D. W. Quinn, The method of characteristics applied to a stochastic two-stage model of carcinogenesis. Mathematical and Computer Modelling. 25(1997) 1–13.

[4] S. H. Moolgavkar, D. J. Venzon, Two-event models for carcinogenesis: incidence curves for childhood and adult tumors. Mathematical Biosciences. 47(1979) 55–77.

DOI: 10.1016/0025-5564(79)90005-1

[5] W. Y. TAN,. A Nonhomogeneous Two-Stage Carcinogenesis Model, Mathl. Modelling. 9(1987) 631-642.

[6] P. Tirupathi Rao, J. Jayabharathiraj, B.N. Naveen Kumar, C. L. Usha, P. Rajasekhara Reddy, Stochastic Modelling of Tumor Growth within Organ during chemotherapy using Bivariate Birth, Death and Migration Processes, IOSR Journal of Mathematics. 10(2014).

DOI: 10.9790/5728-10330108

[7] B. G. Birkhead, The Transient Solution of the Linear Birth-Death Process with Random Spontaneous Mutation, Mathematical Biosciences. 82(1986) 193-200.

DOI: 10.1016/0025-5564(86)90137-9

[8] S. H. Moolgavkar, Model for human carcinogenesis: action of environmental agents, Environmental Health Perspectives. 50(1983) 285–91.

DOI: 10.2307/3429560

[9] B. P. Armitage, The Statistical theory of bacterial populations subject to mutation. Journal of the Royal Statistical Society, 14(1952) 1–40.

[10] A.T. Bharucha-Reid, Elements of the theory of markov processes and their applications, New York, McGraw-Hill, (1960).

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