Mathematical modeling of the second tumors formation and estimation of the distribution of the anti-oncogenes among humans

The relevance of the work is caused by the fact the cancer is a significant factor in human mortality, and cancer incidence is increasing worldwide. As a consequence, the study of the process of carcinogenesis in general and Second tumors, in particular, is an important issue for medical physics. The aim of this study was to uncover the regularities of the secondary tumors formation in cancer patients. Such a study should enable the solution of a number of related problems, viz. estimation of the distribution of the a-genes among humans, which damage seems to be one of the most essential factors of carcinogenesis. To achieve the aim of the study the probabilistic mathematical modeling was employed, resulting in the generation of the mathematical models, capable of estimating such probabilities: 1) probability of the second tumor formation in a patient at some age, provided that the first tumor is formed in this patient at certain age; 2) probability of two tumors formation in a patient at certain age. Furthermore, the proposed models enable employment of the statistics of the second tumors to refine the parameters of the carcinogenesis model. In conclusion, the probabilistic mathematical modeling allows evaluation of a number of important quantitative characteristics of the carcinogenesis.