ABSTRACT
This chapter considers multiple pathway models of carcinogenesis involving one-stage models and two-stage models. It aims to develop the mathematical theories of multiple pathway models of carcinogenesis. Since mutation rates are usually very small so that pathways involving three or more stages are usually dominated by one-stage and two-stage pathways, in the mathematical derivations we thus restrict ourselves only to multiple pathway models involving one-stage models and two-stage models. The chapter presents some biological evidence supporting multiple pathway models involving one-stage models and two-stage models. Based on the biological evidence, it proposes a stochastic multiple pathway model involving one-stage and two two-stage models. The chapter considers some special cases in each of which they derive the probability generating functions and the incidence functions of tumors. These special cases include a semi-homogeneous model, a piece-wise semi-homogeneous model and a multiple pathway model involving one one-stage and one two-stage models. Finally, some possible applications of the multiple pathway models are indicated.
