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

Abstract

Abstract. 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.