메뉴 건너뛰기




Volumn 47, Issue 1-2, 2008, Pages 196-209

On the kinetic theory for active particles: A model for tumor-immune system competition

Author keywords

Active particles; Biology; Cauchy problem; Kinetic theory; Living systems; Nonlinearity

Indexed keywords

CELLS; IMMUNOLOGY; KINETIC THEORY; MATHEMATICAL MODELS; ONCOLOGY;

EID: 35348966161     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.02.016     Document Type: Article
Times cited : (24)

References (29)
  • 1
    • 0026932946 scopus 로고
    • On the distribution of dominance in populations of social organisms
    • Jager E., and Segel L. On the distribution of dominance in populations of social organisms. SIAM J. Appl. Math. 52 5 (1992) 1442-1468
    • (1992) SIAM J. Appl. Math. , vol.52 , Issue.5 , pp. 1442-1468
    • Jager, E.1    Segel, L.2
  • 2
    • 0033166360 scopus 로고    scopus 로고
    • From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications
    • Arlotti L., Bellomo N., and Latrach K. From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications. Math. Comput. Modelling 30 1-2 (1999) 15-40
    • (1999) Math. Comput. Modelling , vol.30 , Issue.1-2 , pp. 15-40
    • Arlotti, L.1    Bellomo, N.2    Latrach, K.3
  • 3
    • 0028120597 scopus 로고
    • Dynamics of tumor interaction with the host immune system
    • Bellomo N., and Forni G. Dynamics of tumor interaction with the host immune system. Math. Comput. Modelling 20 1 (1994) 107-122
    • (1994) Math. Comput. Modelling , vol.20 , Issue.1 , pp. 107-122
    • Bellomo, N.1    Forni, G.2
  • 4
    • 0037296957 scopus 로고    scopus 로고
    • Qualitative analysis of a mean field model of tumor-immune system competition
    • De Angelis E., and Jabin P.E. Qualitative analysis of a mean field model of tumor-immune system competition. Math. Models Methods Appl. Sci. 13 2 (2003) 187-206
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , Issue.2 , pp. 187-206
    • De Angelis, E.1    Jabin, P.E.2
  • 5
    • 8744228120 scopus 로고    scopus 로고
    • Analysis of a new model for tumor-immune system competition including long-time scale effects
    • Derbel L. Analysis of a new model for tumor-immune system competition including long-time scale effects. Math. Models Methods Appl. Sci. 14 11 (2004) 1657-1681
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.11 , pp. 1657-1681
    • Derbel, L.1
  • 6
    • 26844512863 scopus 로고    scopus 로고
    • A mathematical model of cellular immune response to leukemia
    • Kolev M. A mathematical model of cellular immune response to leukemia. Math. Comput. Modelling 41 10 (2005) 1071-1082
    • (2005) Math. Comput. Modelling , vol.41 , Issue.10 , pp. 1071-1082
    • Kolev, M.1
  • 7
    • 27744605399 scopus 로고    scopus 로고
    • Mathematical models of therapeutical actions related to tumour and immune system competition
    • De Angelis E., and Jabin P.E. Mathematical models of therapeutical actions related to tumour and immune system competition. Math. Methods Appl. Sci. 28 17 (2005) 2061-2083
    • (2005) Math. Methods Appl. Sci. , vol.28 , Issue.17 , pp. 2061-2083
    • De Angelis, E.1    Jabin, P.E.2
  • 8
    • 26844505021 scopus 로고    scopus 로고
    • A mathematical model for single cell cancer-immune system dynamics
    • Kolev M., Kozlowska E., and Lachowicz M. A mathematical model for single cell cancer-immune system dynamics. Math. Comput. Modelling 41 10 (2005) 1083-1095
    • (2005) Math. Comput. Modelling , vol.41 , Issue.10 , pp. 1083-1095
    • Kolev, M.1    Kozlowska, E.2    Lachowicz, M.3
  • 9
    • 27644478289 scopus 로고    scopus 로고
    • Mathematical methods and tools of kinetic theory towards modelling complex biological systems
    • Bellouquid A., and Delitala M. Mathematical methods and tools of kinetic theory towards modelling complex biological systems. Math. Models Methods. Appl. Sci. 15 11 (2005) 1639-1666
    • (2005) Math. Models Methods. Appl. Sci. , vol.15 , Issue.11 , pp. 1639-1666
    • Bellouquid, A.1    Delitala, M.2
  • 10
    • 33750102084 scopus 로고    scopus 로고
    • On the discrete kinetic theory for active particles. Modelling the immune competition
    • Brazzoli I., and Chauviere A. On the discrete kinetic theory for active particles. Modelling the immune competition. Comput. Math. Meth. Med. 7 2-3 (2006) 143-157
    • (2006) Comput. Math. Meth. Med. , vol.7 , Issue.2-3 , pp. 143-157
    • Brazzoli, I.1    Chauviere, A.2
  • 11
    • 2542432804 scopus 로고    scopus 로고
    • Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition
    • Bellomo N., Bellouquid A., and Delitala M. Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Math. Models Methods Appl. Sci. 14 11 (2004) 1683-1733
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.11 , pp. 1683-1733
    • Bellomo, N.1    Bellouquid, A.2    Delitala, M.3
  • 14
    • 27844440786 scopus 로고    scopus 로고
    • Why is mathematical biology so hard?
    • Reed M.C. Why is mathematical biology so hard?. Notices Amer. Math. Soc. 51 3 (2004) 338-342
    • (2004) Notices Amer. Math. Soc. , vol.51 , Issue.3 , pp. 338-342
    • Reed, M.C.1
  • 15
    • 33746069282 scopus 로고    scopus 로고
    • Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems
    • Bellomo N., and Forni G. Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems. Math. Models Methods Appl. Sci. 16 7 (2006) 1001-1029
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 , pp. 1001-1029
    • Bellomo, N.1    Forni, G.2
  • 16
    • 33750097798 scopus 로고    scopus 로고
    • Preface in: Multiscale Cancer Modelling
    • (special issue)
    • Bellomo N., and Sleeman B. Preface in: Multiscale Cancer Modelling. Comput. Math. Meth. Med. 7 2-3 (2006) 67-70 (special issue)
    • (2006) Comput. Math. Meth. Med. , vol.7 , Issue.2-3 , pp. 67-70
    • Bellomo, N.1    Sleeman, B.2
  • 17
    • 33750037333 scopus 로고    scopus 로고
    • Preface in: Cancer Modeling (II)
    • (special issue)
    • Bellomo N., and Maini P. Preface in: Cancer Modeling (II). Math. Models Methods Appl. Sci. 16 7b (2006) iii-vii (special issue)
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 b
    • Bellomo, N.1    Maini, P.2
  • 18
    • 33646148037 scopus 로고    scopus 로고
    • Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles
    • De Angelis E., and Delitala M. Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles. Math. Comput. Modelling 43 11-12 (2006) 1310-1328
    • (2006) Math. Comput. Modelling , vol.43 , Issue.11-12 , pp. 1310-1328
    • De Angelis, E.1    Delitala, M.2
  • 19
    • 33751401909 scopus 로고    scopus 로고
    • Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity
    • De Lillo S., Salvatori M.C., and Bellomo N. Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity. Math. Comput. Modelling 45 5-6 (2007) 564-578
    • (2007) Math. Comput. Modelling , vol.45 , Issue.5-6 , pp. 564-578
    • De Lillo, S.1    Salvatori, M.C.2    Bellomo, N.3
  • 20
    • 2942526841 scopus 로고    scopus 로고
    • A new biology for a new century
    • Woese C.R. A new biology for a new century. Microbiol. Mol. Biol. Rev. 68 2 (2004) 173-186
    • (2004) Microbiol. Mol. Biol. Rev. , vol.68 , Issue.2 , pp. 173-186
    • Woese, C.R.1
  • 21
    • 0036852241 scopus 로고    scopus 로고
    • Cancer immunoediting: from immunosurveillance to tumor escape
    • Dunn G.P., Bruce A.T., Ikeda H., Old L.J., and Schreiber R.D. Cancer immunoediting: from immunosurveillance to tumor escape. Nat. Immunol. 3 11 (2002) 991-998
    • (2002) Nat. Immunol. , vol.3 , Issue.11 , pp. 991-998
    • Dunn, G.P.1    Bruce, A.T.2    Ikeda, H.3    Old, L.J.4    Schreiber, R.D.5
  • 22
    • 21844440052 scopus 로고    scopus 로고
    • Tuning immune responses: diversity and adaptation of the immunological synapse
    • Friedl P., den Boer A.T., and Gunzer M. Tuning immune responses: diversity and adaptation of the immunological synapse. Nat. Rev. Immunol. 5 7 (2005) 532-545
    • (2005) Nat. Rev. Immunol. , vol.5 , Issue.7 , pp. 532-545
    • Friedl, P.1    den Boer, A.T.2    Gunzer, M.3
  • 24
    • 0842288340 scopus 로고    scopus 로고
    • Evolutionary dynamics of biological games
    • Novak M.A., and Sigmund K. Evolutionary dynamics of biological games. Science 303 5659 (2004) 793-799
    • (2004) Science , vol.303 , Issue.5659 , pp. 793-799
    • Novak, M.A.1    Sigmund, K.2
  • 25
    • 4043181214 scopus 로고    scopus 로고
    • Cancer genes and the pathways they control
    • Vogelstein B., and Kinzler K.W. Cancer genes and the pathways they control. Nat. Med. 10 8 (2004) 789-799
    • (2004) Nat. Med. , vol.10 , Issue.8 , pp. 789-799
    • Vogelstein, B.1    Kinzler, K.W.2
  • 26
    • 33750058285 scopus 로고    scopus 로고
    • Existence of a solution to the cell division eigenproblem
    • Michel P. Existence of a solution to the cell division eigenproblem. Math. Models Methods Appl. Sci. 16 7b (2006) 1125-1153
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 b , pp. 1125-1153
    • Michel, P.1
  • 28
    • 33846985641 scopus 로고    scopus 로고
    • Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics
    • Cattani C., and Ciancio A. Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics. Math. Models Methods Appl. Sci. 17 2 (2007) 171-188
    • (2007) Math. Models Methods Appl. Sci. , vol.17 , Issue.2 , pp. 171-188
    • Cattani, C.1    Ciancio, A.2
  • 29
    • 33747088162 scopus 로고    scopus 로고
    • Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy
    • D'Onofrio A. Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy. Math. Models Methods Appl. Sci. 16 8 (2006) 1375-1401
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.8 , pp. 1375-1401
    • D'Onofrio, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.