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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749 . Open Access


A Two-Stage Mutation Stochastic Model of Carcinogenesis Driven by a Three Level Environmental Process

A Two-Stage Mutation Stochastic Model of Carcinogenesis Driven by a Three Level Environmental Process

V. S. S. Yadavalli
Department of Industrial and System Engineering, University of Pretoria, Pretoria 0002, South Africa.

S. Udayabaskaran
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600062, India.

C. T. Dora Pravina
Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600062, India.

S. Sreelakshmi
Department of Engineering Mathematics, HKBK College of Engineering, Bangalore 560045, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.6.109

Received on May 07, 2020
  ;
Accepted on August 18, 2020

Abstract

A two-mutation model of carcinogenesis which evolves under the influence of three level random environment on the production process is formulated and analyzed. A random environment occupies one of the levels 1, 2 and 3 at any time t according to a Markov process. When the environment is in level 1, a normal cell either divides into two normal cells or dies; and an intermediate cell divides into two intermediate cells or dies. When the environment is in level 2, a normal cell either divides into one normal cell and one intermediate cell or dies and an intermediate cell either divides into one intermediate cell and one malignant cell or dies. When the environment is in level 3, a normal cell either divides into two intermediate cells or dies and an intermediate cell either divides into two malignant cells or dies. It is assumed that, once a malignant cell is produced, it generates a malignant tumor with probability 1. We obtain the mean numbers of normal, intermediate and malignant cells at any time t.

Keywords- Age-dependent two-stage stochastic model, Normal cell, Intermediate cell, Malignant cell, Random environment.

Citation

Yadavalli, V. S. S., Udayabaskaran, S., Pravina, C. T. D., & Sreelakshmi, S. (2020). A Two-Stage Mutation Stochastic Model of Carcinogenesis Driven by a Three Level Environmental Process. International Journal of Mathematical, Engineering and Management Sciences, 5(6), 1468-1487. https://doi.org/10.33889/IJMEMS.2020.5.6.109.