Some Stochastic Models for Cancer Cell Growth: Studies on Cancer Modeling

This book is designed to provide the stochastic models for cancer cell growth as an alternative of non-parametric approach of assessing the cancer severity. Much emphasis of modeling is focused to formulation of mathematical models with probabilistic measures on the pathophysiology and genetic properties of cancer. The study is stressed more on stochastic modeling of cancer growth as modeling with deterministic environment is far from the reality. Bivariate stochastic model for normal and mutant cell growth was developed under the assumption of the growth and loss processes of mutant and normal cells are Poisson. Approach of difference differential equations is adopted to obtain the probability functions and several statistical measures. Another stochastic model for mutant and normal cell growth under chemotherapy is developed by taking similar assumptions. Two stage stochastic models for a cancer cell growth with the assumption of (i) every malignant tumor will have the premalignant and malignant clones and (ii) the growth of premalignant cell, mutation and loss of premalignant and malignant cells are random and follows Poisson processes, were developed.