Registro:

Referencias:

• Folkman, J., Angiogenesis (2003) Encyclopedia of Genetics, pp. 66-73
• Folkman, J., Klagsbrun, M., Angiogenic factors (1987) Science, 235 (4787), pp. 442-447
• Liersch, R., Berdel, W., Kessler, T., Angiogenesis inhibition (2010) Recent Results in Cancer Research, 17, p. 231. , 1st edition
• Hahnfeldt, P., Panigrahy, D., Folkman, J., Hlatky, L., Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy (1999) Cancer Research, 59 (19), pp. 4770-4775
• Andersen, L.K., Mackey, M.C., Resonance in periodic chemotherapy: A case study of acute myelogenous leukemia (2001) Journal of Theoretical Biology, 209 (1), pp. 113-130. , DOI 10.1006/jtbi.2000.2255
• Liu, Z., Zhong, S., Yin, C., Chen, W., Permanence, extinction and periodic solutions in a mathematical model of cell populations affected by periodic radiation (2011) Applied Mathematics Letters, 24, pp. 1745-1750
• Swierniak, A., Kimmel, M., Smieja, J., Mathematical modeling as a tool for planning anticancer therapy (2009) European Journal of Pharmacology, 625, pp. 108-121
• Macklin, P., Lowengrub, J., Nonlinear simulation of the effect of microenvironment on tumor growth (2007) Journal of Theoretical Biology, 245 (4), pp. 677-704. , DOI 10.1016/j.jtbi.2006.12.004, PII S0022519306005649
• Kuang, Y., (1993) Delay Differential Equations with Applications in Population Dynamics, 191. , Mathematics in Science and Engineering Academic Press, Inc. Boston, MA
• Andrew, S.M., Baker, C.T.H., Bocharov, G.A., Rival approaches to mathematical modelling in immunology (2007) Journal of Computational and Applied Mathematics, 205 (2), pp. 669-686. , DOI 10.1016/j.cam.2006.03.035, PII S037704270600392X
• Banerjee, S., Sarkar, R.R., Delay-induced model for tumor-immune interaction and control of malignant tumor growth (2008) BioSystems, 91 (1), pp. 268-288. , DOI 10.1016/j.biosystems.2007.10.002, PII S0303264707001499
• Byrne, H.M., The effect of time delays on the dynamics of avascular tumor growth (1997) Mathematical Biosciences, 144 (2), pp. 83-117. , DOI 10.1016/S0025-5564(97)00023-0, PII S0025556497000230
• D'Onofrio, A., Gatti, F., Cerrai, P., Freschi, L., Delay-induced oscillatory dynamics of tumour immune system interaction (2010) Mathematical and Computer Modelling, 51, pp. 572-591
• Xu, S., Analysis of a delayed mathematical model for tumor growth (2010) Nonlinear Analysis: Real World Applications, 11, pp. 4121-4127
• Sachs, R.K., Hlatky, L.R., Hahnfeldt, P., Simple ODE models of tumor growth and anti-angiogenic or radiation treatment (2001) Mathematical and Computer Modelling, 33 (12-13), pp. 1297-1305. , DOI 10.1016/S0895-7177(00)00316-2, PII S0895717700003162
• Restsky, M.W., Swartzendruber, D.E., Wardwell, R.H., Bame, P.D., Is Gompertzian or exponential kinetics a valid description of individual human cancer growth? (1990) Medical Hypotheses, 33 (2), pp. 95-106. , DOI 10.1016/0306-9877(90)90186-I
• Araujo, R.P., McElwain, D.L.S., A history of the study of solid tumour growth: The contribution of mathematical modelling (2004) Bulletin of Mathematical Biology, 66 (5), pp. 1039-1091. , DOI 10.1016/j.bulm.2003.11.002, PII S0092824003001265
• D'Onofrio, A., Metamodeling tumor immune system interaction, tumor evasion and immunotherapy (2008) Mathematical and Computer Modelling, 47, pp. 614-637
• Amster, P., Berezansky, L., Idels, L., Stability of hahnfeldt angiogenesis models with time lags (2011) Mathematical and Computer Modelling, , arxiv:1105.3260v1
• Berezansky, L., Braverman, E., Domoshnitsky, A., Stability of the second order delay differential equations with a damping term (2008) Differential Equations and Dynamical Systems, 16, pp. 3-24
• Diblik, J., Koksch, N., Sufficient conditions for the existence of global solutions of delayed differential equations (2006) Journal of Mathematical Analysis and Applications, 318 (2), pp. 611-625. , DOI 10.1016/j.jmaa.2005.06.020, PII S0022247X05005664
• Gyori, I., Hartung, F., Fundamental solution and asymptotic stability of linear delay differential equations (2006) Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 13 (2), pp. 261-287
• Krisztin, T., Global dynamics of delay differential equations (2008) Periodica Mathematica Hungarica, 56, pp. 83-95
• Muroya, Y., Global stability for separable nonlinear delay differential systems (2007) Journal of Mathematical Analysis and Applications, 326 (1), pp. 372-389. , DOI 10.1016/j.jmaa.2006.01.094, PII S0022247X06002277
• Sherera, E., Hannemanna, R., Rundellb, A., Ramkrishnaa, D., Analysis of resonance chemotherapy in leukemia treatment via multi-staged population balance models (2006) Journal of Theoretical Biology, 240, pp. 648-661
• Alzabut, J., Nieto, J., Stamov, G., Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis (2009) Boundary Value Problems, pp. 1-10
• Bellouquid, A., De Angelis, E., From kinetic models of multicellular growing systems to macroscopic biological tissue models (2011) Nonlinear Analysis: Real World Applications, 12, pp. 1111-1122
• Delgado, M., Gayte, I., Morales-Rodrigo, C., Suarez, A., An angiogenesis model with nonlinear chemotactic response and flux at the tumor boundary (2010) Nonlinear Analysis: Theory, Methods & Applications, 72, pp. 330-347
• Delgado, M., Morales-Rodrigo, C., Suarez, A., Tello, J., On a parabolic-elliptic chemotactic model with coupled boundary conditions (2010) Nonlinear Analysis: Real World Applications, 11, pp. 3884-3902
• Ito, A., Gokieli, M., Niezgodka, M., Szyman'Ska, Z., Local existence and uniqueness of solutions to approximate systems of 1D tumor invasion model (2010) Nonlinear Analysis: Real World Applications, 11, pp. 3555-3566
• Kassara, K., Moustafid, A., Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method (2011) Mathematical Biosciences, 231, pp. 135-143
• Tao, Y., Global existence for a haptotaxis model of cancer invasion with tissue remodeling (2011) Nonlinear Analysis: Real World Applications, 12, pp. 418-435
• Wei, X., Cui, S., Existence and uniqueness of global solutions for a mathematical model of antiangiogenesis in tumor growth (2008) Nonlinear Analysis: Real World Applications, 9, pp. 1827-1836
• Wei, X., Guo, C., Global existence for a mathematical model of the immune response to cancer (2010) Nonlinear Analysis: Real World Applications, 11, pp. 3903-3911
• Lloyd, N., (1978) Degree Theory, , Cambridge University. Press Cambridge
• Mawhin, J., (1979) Topological Degree Methods in Nonlinear Boundary Value Problems, 40. , CBMS Regional Conference Series in Mathematics Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 915, 1977 American Mathematical Society Providence, RI
• Ronto, M., Trofimchuk, S., Numerical-analytic method for non-linear differential equations (1998) Public University of Miskolc, Series D, 38, pp. 97-116

Citas:

---------- APA ----------

---------- CHICAGO ----------

---------- MLA ----------

---------- VANCOUVER ----------