An Early Detection Model for a Brain Tumor-Is (Immune System) Interaction with Fuzzy Initial Values

In this paper, we adopt a model by including fuzzy initial values to study the interaction of a monoclonal brain tumor and the macrophages for an early detection treatment. Numerical simulations will give detailed information on the behavior of the model at the end of the paper. We perform all the computations in this study with the help of the Maple software.

[1]  I. Burhan Türksen,et al.  An algorithm for the solution of second order fuzzy initial value problems , 2013, Expert Syst. Appl..

[2]  Ömer Oruç,et al.  A PREY PREDATOR MODEL WITH FUZZY INITIAL VALUES , 2012 .

[3]  Eyke Hüllermeier,et al.  An Approach to Modelling and Simulation of Uncertain Dynamical Systems , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[4]  Congxin Wu,et al.  On Henstock integral of fuzzy-number-valued functions (I) , 2001, Fuzzy Sets Syst..

[5]  Goreti Marreiros,et al.  Quality in Hospital Administrative Databases , 2014 .

[6]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

[7]  Salvatore Torquato,et al.  A Cellular Automaton Model of Brain Tumor Treatment and Resistance , 2002 .

[8]  Barnabás Bede,et al.  Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations , 2005, Fuzzy Sets Syst..

[9]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[10]  Goldie Jh,et al.  A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate. , 1979 .

[11]  Ahmad Muhammad Zaini,et al.  A predator prey model with Fuzzy initial populations , 2009 .

[12]  E. Holland,et al.  Glioblastoma multiforme: the terminator. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Awad El-Gohary,et al.  Chaos and optimal control of cancer self-remission and tumor system steady states☆ , 2008 .

[14]  Sorin G. Gal Approximation Theory in Fuzzy Setting , 2000 .

[15]  F. Bozkurt Stability Analysis of a Fractional-Order Differential Equation System of a GBM-IS Interaction Depending on the Density , 2014 .

[16]  Imre J. Rudas,et al.  First order linear fuzzy differential equations under generalized differentiability , 2007, Inf. Sci..

[17]  A. Khastan,et al.  New Results on Multiple Solutions for th-Order Fuzzy Differential Equations under Generalized Differentiability , 2009 .

[18]  H. Román-Flores,et al.  On new solutions of fuzzy differential equations , 2008 .

[19]  Osmo Kaleva Fuzzy differential equations , 1987 .

[20]  Rodney Carlos Bassanezi,et al.  Predator–prey fuzzy model , 2008 .

[21]  F. Benli,et al.  A tumor-macrophage interaction model with fuzzy initial values , 2015 .

[22]  Yijun Lou,et al.  Global dynamics of a predator–prey model , 2010 .

[23]  Fatma Bozkurt Modeling a Tumor Growth with Piecewise Constant Arguments , 2013 .