A full fuzzy generalized mathematical model of tumor growth and its analysis

Mathematical modelling as a useful technique to obtain a better and wider perception of a complex biological subject such as cancer, has been increasingly applied in recent years. Since the parameters of a mathematical model are obtained by observations and measurements, they are exposed to errors and have uncertainty and ambiguity in their nature. In this paper, in order to achieve a more realistic mathematical model of tumor growth, a system of integro-partial differential equations which describes the growth of a tumor characterized by the presence of cancer stem cells - which are the main reason of treatment failure and tumor relapse - is generalized to a fuzzy integro-partial differential system. Introducing some definitions, several theorems are proved to convert the fuzzy integro-partial differential system to an optimization problem. The proposed new method computes not only the approximate fuzzy solution of the full fuzzy system, but also the difference between the exact and approximate solution. It is further found that the tumor growth paradox appears in the full fuzzy mathematical model of tumor growth as well.