Mathematical bridge between epidemiological and molecular data on cancer and beyond

Abstract

AbstractMathematical models of cancer growth have been subject of research for many years. At least six different mathematical models and their countless variations and combinations have been published till date in scientific literature that reasonably explains epidemiological prediction of multi-step carcinogenesis. Each one deals with a particular set of problems at a given organizational level ranging from populations to genes. None of the articles have incorporated all the types of cancers. Any of the models adopted in those articles so far does not account for both epidemiological and molecular levels of carcinogenesis. In other words, those models are used in ‘specialized’ ways to focus on specific attributes of cancer.Therefore, our work aims at the derivation of a mathematical model consisting of fewer than five equations that reasonably explains epidemiological prediction of multi-step carcinogenesis. We have come up with a mathematically rigorous system to derive those equations that satisfies the basic assumptions of both epidemiology and molecular biology without having to incorporate arbitrary numerical coefficients or constants devoid of any causal explanation just to fit the empirical data. After satisfactorily generalizing all the epidemiological and molecular data, we attempted to apply the model for non-neoplastic conditions satisfying the set of assumptions mathematically equivalent to multi-step carcinogenesis. The aim of this treatise is not only to provide some novel insight into mathematical modeling of malignant transformation, but also to revive the classical tools we already have at our disposal to pave the way towards novel insight into integrated approach in cancer research.