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Recognition and learning in a mathematical model for immune response against cancer
1.  Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy, Italy 
References:
[1] 
E. Agliari, A. Barra, F. Guerra and F. Moauro, A thermodynamical perspective of immune capabilities, J. Theor. Biol., 287 (2010), 4863. 
[2] 
N. Bellomo and M. Delitala, From the mathematical kinetic, and stochastic game theory to modeling mutations, onset, progression and immune competition of cancer cells, Phys. Life Rev., 5 (2008), 183206. 
[3] 
A. Bellouquid and M. Delitala, "Modelling Complex Multicellular Systems  A Kinetic Theory Approach,'' Birkhäuser, Boston, 2006. 
[4] 
C. Bianca and M. Delitala, On the modelling genetic mutations and immune system competition, Comput. Math. Appl., 61 (2011) 23622375. doi: 10.1016/j.camwa.2011.01.024. 
[5] 
S. BunimovichMendrazitsky, H. Byrne and L. Stone, Mathematical model of pulsed immunotherapy for superficial bladder cancer, Bull. Math. Biol., 70 (2008), 20552076. doi: 10.1007/s115380089344z. 
[6] 
R. E. Callard and A. J. Yates, Immunology and mathematics: Crossing the divide, Immunology, 115 (2005), 2133. 
[7] 
V. Calvez, A. Korobeinikov and P. K. Maini, Cluster formation for multistrain infections with crossimmunity, J. Theor. Biol., 233 (2005), 7583. doi: 10.1016/j.jtbi.2004.09.016. 
[8] 
C. Cattani, A. Ciancio and A. d'Onofrio, Metamodeling the learninghiding competition between tumours and the immune system: A kinematic approach, Math. Comput. Model., 52 (2010), 6269. doi: 10.1016/j.mcm.2010.01.012. 
[9] 
A. K. Chakraborty, M. L. Dustin and A. S. Shaw, In Silico models in molecular and cellular immunology: Successes, promises, and challenges, Nat. Immunol., 4 (2003), 933936. 
[10] 
A. K. Chakraborty and A. Kosmrlj, Statistical mechanical concepts in immunology, Annu. Rev. Phys. Chem., 61 (2010), 283303. 
[11] 
M. A. J. Chaplain and A. Matzavinos, Mathematical modelling of spatiotemporal phenomena in tumour immunology, Lect. Notes Math., 1872 (2006), 131183, SpringerVerlag Berlin Heidelberg. doi: 10.1007/11561606_4. 
[12] 
D. Chowdhury, M. Sahimi and D. Stauffer, A discrete model for immune surveillance, tumor immunity and cancer, J. Theor. Biol., 152 (1991), 263270. 
[13] 
L. G. de Pillis, D. G. Mallet and A. E. Radunskaya, Spatial tumorimmune modeling, Comput. Math. Methods Med., 7 (2006), 159176. doi: 10.1080/10273660600968978. 
[14] 
M. Delitala and T. Lorenzi, A mathematical model for the dynamics of cancer hepatocytes under therapeutic actions, J. Theor. Biol., 297 (2012), 88102. doi: 10.1016/j.jtbi.2011.11.022. 
[15] 
L. Desvillettes, P. E. Jabin, S. Mischler and G. Raoul, On selection dynamics for continuous structured populations, Commun. Math. Sci., 6 (2008), 729747. 
[16] 
G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape, Nat. Immunol., 3 (2002), 991998. 
[17] 
P. A. W. Edwards, Heterogeneous expression of cellsurface antigens in normal epithelia and their tumours, revealed by monoclonal antibodies, Br. J. Cancer, 51 (1985), 149160. 
[18] 
S. Eikenberry, C. Thalhauser and Y. Kuang, Tumorimmune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma, PLoS Comput. Biol., 5 (2009), e1000362. doi: 10.1371/journal.pcbi.1000362. 
[19] 
A. H. L. Erickson, A. Wise, S. Fleming, M. Baird, Z. Lateef, A. Molinaro, M. TebohEwungkem and L. de Pillis, A preliminary mathematical model of skin dendritic cell tracking and induction of t cell immunity, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 323336. doi: 10.3934/dcdsb.2009.12.323. 
[20] 
D. Hanahan and R. A. Weinberg, Hallmarks of cancer: the next generation, Cell, 144 (2011), 646674. 
[21] 
M. Herrero, On the role of mathematics in biology, J. Math. Biol., 54 (2007), 887889. doi: 10.1007/s0028500700955. 
[22] 
W. Hu, W. Zhong, F. Wang, L. Li and Y. Shao, In silico synergism and antagonism of an antitumour system intervened by coupling immunotherapy and chemotherapy: A mathematical modelling approach, Bull. Math. Biol., (2011). doi: 10.1007/s115380119693x. 
[23] 
M. Kaufman, J. Urbain and R. Thomas, Towards a logical analysis of the immune response, J. Theor. Biol., 114 (1985), 527561. doi: 10.1016/S00225193(85)800424. 
[24] 
T. J. Kindt, R. A. Goldsby, B. A. Osborne and J. Kuby, "Kuby Immunology," W. H. Freeman and Company, 2005. 
[25] 
M. Kolev, Mathematical modeling of the competition between acquired immunity and cancer, Int. J. Appl. Math. Comput. Sci., 13 (2003), 289296. 
[26] 
V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bull. Math. Biol., 56 (1994), 295321. 
[27] 
J. Kzhyshkowska, A. MarciniakCzochra and A. Gratchev, Perspectives of mathematical modelling for understanding of macrophage function, Immunobiology, 212 (2007), 813825. 
[28] 
D. G. Mallet and L. G. de Pillis, A cellular automata model of tumorimmune system interactions, J. Theor. Biol., 239 (2006), 334350. doi: 10.1016/j.jtbi.2005.08.002. 
[29] 
D. Mason, A very high level of crossreactivity is an essential feature of the Tcell receptor, Immunology today, 19 (1998), 395404. 
[30] 
A. Matzavinos, M. A.J . Chaplain and V. A. Kuznetsov, Mathematical modelling of the spatiotemporal response of cytotoxic Tlymphocytes to a solid tumor, Math. Med. Biol., 21 (2004), 134. 
[31] 
L. M. Merlo, J. W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nat. Rev. Cancer, 6 (2006), 924935. 
[32] 
R. K. Oldham and R. O. Dillman (Eds.), "Principles of Cancer Biotherapy,'' $3^{rd}$ edition, Kluwer Academic Publishers, The Netherlands, 1997. 
[33] 
F. Pappalardo, S. Musumeci and S. Motta, Modeling immune system control of atherogenesis, Bioinformatics, 24 (2008), 17151721. 
[34] 
A. Perelson and G. Weisbuch, Immunology for physicists, Rev. Mod. Phys., 69 (1997), 12191268. 
[35] 
B. Perthame, "Transport Equations in Biology,'' Birkhäuser, Basel, 2007. 
[36] 
A. Plesa , G. Ciuperca, S. Genieys, V. Louvet, L. PujoMenjouet, C. Dumontet and V. Volpert, Diagnostics of the AML with immunophenotypical data, Math. Mod. Nat. Phen., 2 (2006), 104123. doi: 10.1051/mmnp:2008006. 
[37] 
W. R. Welch, J. M. Niloff, D. Anderson, A. Battailea, S. Emery, R. C. Knapp and R. C. Bast, Antigenic heterogeneity in human ovarian cancer, Gynecol. Oncol., 38 (1990), 1216. 
[38] 
L. Wooldridge, J. EkerucheMakinde, H. A. van den Berg, A. Skowera, J. J. Miles, M. P. Tan, G. Dolton, M. Clement, S. LlewellynLacey, D. A. Price, et al., A single autoimmune t cell receptor recognizes more than a million different peptides, Journal of Biological Chemistry, 287 (2012), 11681177. 
show all references
References:
[1] 
E. Agliari, A. Barra, F. Guerra and F. Moauro, A thermodynamical perspective of immune capabilities, J. Theor. Biol., 287 (2010), 4863. 
[2] 
N. Bellomo and M. Delitala, From the mathematical kinetic, and stochastic game theory to modeling mutations, onset, progression and immune competition of cancer cells, Phys. Life Rev., 5 (2008), 183206. 
[3] 
A. Bellouquid and M. Delitala, "Modelling Complex Multicellular Systems  A Kinetic Theory Approach,'' Birkhäuser, Boston, 2006. 
[4] 
C. Bianca and M. Delitala, On the modelling genetic mutations and immune system competition, Comput. Math. Appl., 61 (2011) 23622375. doi: 10.1016/j.camwa.2011.01.024. 
[5] 
S. BunimovichMendrazitsky, H. Byrne and L. Stone, Mathematical model of pulsed immunotherapy for superficial bladder cancer, Bull. Math. Biol., 70 (2008), 20552076. doi: 10.1007/s115380089344z. 
[6] 
R. E. Callard and A. J. Yates, Immunology and mathematics: Crossing the divide, Immunology, 115 (2005), 2133. 
[7] 
V. Calvez, A. Korobeinikov and P. K. Maini, Cluster formation for multistrain infections with crossimmunity, J. Theor. Biol., 233 (2005), 7583. doi: 10.1016/j.jtbi.2004.09.016. 
[8] 
C. Cattani, A. Ciancio and A. d'Onofrio, Metamodeling the learninghiding competition between tumours and the immune system: A kinematic approach, Math. Comput. Model., 52 (2010), 6269. doi: 10.1016/j.mcm.2010.01.012. 
[9] 
A. K. Chakraborty, M. L. Dustin and A. S. Shaw, In Silico models in molecular and cellular immunology: Successes, promises, and challenges, Nat. Immunol., 4 (2003), 933936. 
[10] 
A. K. Chakraborty and A. Kosmrlj, Statistical mechanical concepts in immunology, Annu. Rev. Phys. Chem., 61 (2010), 283303. 
[11] 
M. A. J. Chaplain and A. Matzavinos, Mathematical modelling of spatiotemporal phenomena in tumour immunology, Lect. Notes Math., 1872 (2006), 131183, SpringerVerlag Berlin Heidelberg. doi: 10.1007/11561606_4. 
[12] 
D. Chowdhury, M. Sahimi and D. Stauffer, A discrete model for immune surveillance, tumor immunity and cancer, J. Theor. Biol., 152 (1991), 263270. 
[13] 
L. G. de Pillis, D. G. Mallet and A. E. Radunskaya, Spatial tumorimmune modeling, Comput. Math. Methods Med., 7 (2006), 159176. doi: 10.1080/10273660600968978. 
[14] 
M. Delitala and T. Lorenzi, A mathematical model for the dynamics of cancer hepatocytes under therapeutic actions, J. Theor. Biol., 297 (2012), 88102. doi: 10.1016/j.jtbi.2011.11.022. 
[15] 
L. Desvillettes, P. E. Jabin, S. Mischler and G. Raoul, On selection dynamics for continuous structured populations, Commun. Math. Sci., 6 (2008), 729747. 
[16] 
G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape, Nat. Immunol., 3 (2002), 991998. 
[17] 
P. A. W. Edwards, Heterogeneous expression of cellsurface antigens in normal epithelia and their tumours, revealed by monoclonal antibodies, Br. J. Cancer, 51 (1985), 149160. 
[18] 
S. Eikenberry, C. Thalhauser and Y. Kuang, Tumorimmune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma, PLoS Comput. Biol., 5 (2009), e1000362. doi: 10.1371/journal.pcbi.1000362. 
[19] 
A. H. L. Erickson, A. Wise, S. Fleming, M. Baird, Z. Lateef, A. Molinaro, M. TebohEwungkem and L. de Pillis, A preliminary mathematical model of skin dendritic cell tracking and induction of t cell immunity, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 323336. doi: 10.3934/dcdsb.2009.12.323. 
[20] 
D. Hanahan and R. A. Weinberg, Hallmarks of cancer: the next generation, Cell, 144 (2011), 646674. 
[21] 
M. Herrero, On the role of mathematics in biology, J. Math. Biol., 54 (2007), 887889. doi: 10.1007/s0028500700955. 
[22] 
W. Hu, W. Zhong, F. Wang, L. Li and Y. Shao, In silico synergism and antagonism of an antitumour system intervened by coupling immunotherapy and chemotherapy: A mathematical modelling approach, Bull. Math. Biol., (2011). doi: 10.1007/s115380119693x. 
[23] 
M. Kaufman, J. Urbain and R. Thomas, Towards a logical analysis of the immune response, J. Theor. Biol., 114 (1985), 527561. doi: 10.1016/S00225193(85)800424. 
[24] 
T. J. Kindt, R. A. Goldsby, B. A. Osborne and J. Kuby, "Kuby Immunology," W. H. Freeman and Company, 2005. 
[25] 
M. Kolev, Mathematical modeling of the competition between acquired immunity and cancer, Int. J. Appl. Math. Comput. Sci., 13 (2003), 289296. 
[26] 
V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bull. Math. Biol., 56 (1994), 295321. 
[27] 
J. Kzhyshkowska, A. MarciniakCzochra and A. Gratchev, Perspectives of mathematical modelling for understanding of macrophage function, Immunobiology, 212 (2007), 813825. 
[28] 
D. G. Mallet and L. G. de Pillis, A cellular automata model of tumorimmune system interactions, J. Theor. Biol., 239 (2006), 334350. doi: 10.1016/j.jtbi.2005.08.002. 
[29] 
D. Mason, A very high level of crossreactivity is an essential feature of the Tcell receptor, Immunology today, 19 (1998), 395404. 
[30] 
A. Matzavinos, M. A.J . Chaplain and V. A. Kuznetsov, Mathematical modelling of the spatiotemporal response of cytotoxic Tlymphocytes to a solid tumor, Math. Med. Biol., 21 (2004), 134. 
[31] 
L. M. Merlo, J. W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nat. Rev. Cancer, 6 (2006), 924935. 
[32] 
R. K. Oldham and R. O. Dillman (Eds.), "Principles of Cancer Biotherapy,'' $3^{rd}$ edition, Kluwer Academic Publishers, The Netherlands, 1997. 
[33] 
F. Pappalardo, S. Musumeci and S. Motta, Modeling immune system control of atherogenesis, Bioinformatics, 24 (2008), 17151721. 
[34] 
A. Perelson and G. Weisbuch, Immunology for physicists, Rev. Mod. Phys., 69 (1997), 12191268. 
[35] 
B. Perthame, "Transport Equations in Biology,'' Birkhäuser, Basel, 2007. 
[36] 
A. Plesa , G. Ciuperca, S. Genieys, V. Louvet, L. PujoMenjouet, C. Dumontet and V. Volpert, Diagnostics of the AML with immunophenotypical data, Math. Mod. Nat. Phen., 2 (2006), 104123. doi: 10.1051/mmnp:2008006. 
[37] 
W. R. Welch, J. M. Niloff, D. Anderson, A. Battailea, S. Emery, R. C. Knapp and R. C. Bast, Antigenic heterogeneity in human ovarian cancer, Gynecol. Oncol., 38 (1990), 1216. 
[38] 
L. Wooldridge, J. EkerucheMakinde, H. A. van den Berg, A. Skowera, J. J. Miles, M. P. Tan, G. Dolton, M. Clement, S. LlewellynLacey, D. A. Price, et al., A single autoimmune t cell receptor recognizes more than a million different peptides, Journal of Biological Chemistry, 287 (2012), 11681177. 
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