Different initial conditions in fuzzy Tumor model
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Abstract
One of the best ways for better understanding of biological experiments is mathematical modeling. Modeling cancer is one of the complicated biological modeling that has uncertainty. Therefore, fuzzy models have studied because of their application in achievement uncertainty in modeling. Overall, the main purpose of this modeling is creating a new view of complex phenomena. In this paper, fuzzy differential equation model consisting of tumor, the immune system and normal cells has been studied. Model derived from a classical model DePillis in 2003, which some parameters from a clinical point of view can be described in the region. In this model, by considering fuzzy parameters from clinical point of view, the three-dimensional fuzzy tumor cells in terms of time and membership function are pictured and region of uncertainties are determined. To access the uncertainty area we use fuzzy differential inclusion method that is one of the including methods of solving differential equations. Also, different initial conditions on the model are inserted and the results of them are analyzed because tumor has different treatment in different initial conditions. Results show that fuzzy models in the best way justify what happens in the reality.
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