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A simple model of carcinogenic mutations with time delay and diffusion
1.  Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02097 Warsaw 
2.  College of Interfaculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Zwirki i Wigury 93, 02089 Warsaw, Poland 
References:
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J. A. Adam and N. Bellomo, "A Survey of Models for Tumorimune System Synamics," Birkhäuser, Boston, 1997. 
[2] 
R. Ahangar and X. B. Lin, Multistage evolutionary model for carcinogenesis mutations, Electron. J. Diff. Eqns., 10 (2003), 3353. 
[3] 
P. K. Brazhnik and J. J. Tyson, On travelling wave solutions of Fisher's equation in two spatial dimensions, SIAM J. Appl. Math., 60 (1999), 371391. doi: 10.1137/S0036139997325497. 
[4] 
K. L. Cooke and P. van den Driessche, On zeroes of some transcendental equations, Funkcj. Ekvacioj, 29 (1986), 7790. 
[5] 
T. Faria, Stability and bifurcation for a delayed predatorprey model and the effect of diffusion, J. Math. Anal. Appl., 254 (2001), 433463. doi: 10.1006/jmaa.2000.7182. 
[6] 
U. Foryś, Comparison of the models for carcinogenesis mutations  onestage case, in "Proceedings of the Tenth National Conference Application of Mathematics in Biology and Medicine," Świçety Krzy.z, (2004), 1318. 
[7] 
U. Foryś, Time delays in onestage models for carcinogenesis mutations, in "Proceedings of the Eleventh National Conference Application of Mathematics in Biology and Medicine", Zawoja, (2005), 1318. 
[8] 
U. Foryś, Stability analysis and comparison of the models for carcinogenesis mutations in the case of two stages of mutations, J. Appl. Anal., 11 (2005), 200281. doi: 10.1515/JAA.2005.283. 
[9] 
U. Foryś, Multidimensional LotkaVolterra system for carcinogenesis mutations, Math. Meth. Appl. Sci., 32 (2009), 22872308. doi: 10.1002/mma.1137. 
[10] 
J. K. Hale, "Theory of Functional Differential Equations," Springer, 1977. 
[11] 
J. D. Murray, "Mathematical Biology I: An Introduction," Springer, 2002. 
[12] 
J. D. Murray, "Mathematical Biology II: Spatial Models and Biomedical Applications," Springer, 2003. 
[13] 
A. S. Perelson and G. Weisbuch, Immunology for physicists, Rev. Mod. Phys., 69 (1997), 12191267. doi: 10.1103/RevModPhys.69.1219. 
show all references
References:
[1] 
J. A. Adam and N. Bellomo, "A Survey of Models for Tumorimune System Synamics," Birkhäuser, Boston, 1997. 
[2] 
R. Ahangar and X. B. Lin, Multistage evolutionary model for carcinogenesis mutations, Electron. J. Diff. Eqns., 10 (2003), 3353. 
[3] 
P. K. Brazhnik and J. J. Tyson, On travelling wave solutions of Fisher's equation in two spatial dimensions, SIAM J. Appl. Math., 60 (1999), 371391. doi: 10.1137/S0036139997325497. 
[4] 
K. L. Cooke and P. van den Driessche, On zeroes of some transcendental equations, Funkcj. Ekvacioj, 29 (1986), 7790. 
[5] 
T. Faria, Stability and bifurcation for a delayed predatorprey model and the effect of diffusion, J. Math. Anal. Appl., 254 (2001), 433463. doi: 10.1006/jmaa.2000.7182. 
[6] 
U. Foryś, Comparison of the models for carcinogenesis mutations  onestage case, in "Proceedings of the Tenth National Conference Application of Mathematics in Biology and Medicine," Świçety Krzy.z, (2004), 1318. 
[7] 
U. Foryś, Time delays in onestage models for carcinogenesis mutations, in "Proceedings of the Eleventh National Conference Application of Mathematics in Biology and Medicine", Zawoja, (2005), 1318. 
[8] 
U. Foryś, Stability analysis and comparison of the models for carcinogenesis mutations in the case of two stages of mutations, J. Appl. Anal., 11 (2005), 200281. doi: 10.1515/JAA.2005.283. 
[9] 
U. Foryś, Multidimensional LotkaVolterra system for carcinogenesis mutations, Math. Meth. Appl. Sci., 32 (2009), 22872308. doi: 10.1002/mma.1137. 
[10] 
J. K. Hale, "Theory of Functional Differential Equations," Springer, 1977. 
[11] 
J. D. Murray, "Mathematical Biology I: An Introduction," Springer, 2002. 
[12] 
J. D. Murray, "Mathematical Biology II: Spatial Models and Biomedical Applications," Springer, 2003. 
[13] 
A. S. Perelson and G. Weisbuch, Immunology for physicists, Rev. Mod. Phys., 69 (1997), 12191267. doi: 10.1103/RevModPhys.69.1219. 
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