Stochastic Mathematical Models of Carcinogenesis

Geneticists and molecular biologists have demonstrated that carcinogenesis is a stochastic multi-stage process with each cancer tumor being derived from a single stem cell which has sustained a finite number of genetic and/or epigenetic changes (Tan 1991, Wienberg 2007, Tan, Chen and Zhang, 2008). These genetic and/ or epigenetic changes initiate and facilitate cancer progression by driving and disturbing some relevant molecular signal pathways to promote cell proliferation and growth of cancer stem cells. In order for the biological findings to be tested quantitatively against human epidemiological data and animal experimental data, and in order to develop efficient controlling strategies for human cancer, it is absolutely essential that these biological findings be transformed into stochastic mathematical models. This calls for the development of biologically based stochastic mathematical models for human cancers.