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Volumn 12, Issue 4, 2011, Pages 2396-2407

Individually-based Markov processes modeling nonlinear systems in mathematical biology

Author keywords

Integrodifferential equations; Markov jump processes; Microscopic models; Nonlinear ODEs; Nonlinear PDEs

Indexed keywords

APPLIED SCIENCE; BILINEAR EQUATIONS; ERROR ESTIMATES; GENERAL APPROACH; INTERMEDIATE LEVEL; MACROSCOPIC LEVELS; MARKOV JUMP PROCESSES; MATHEMATICAL BIOLOGY; MATHEMATICAL RELATIONSHIP; MESOSCALE LEVELS; MESOSCOPIC LEVELS; MESOSCOPIC MODELS; MICROSCALE LEVELS; MICROSCOPIC MODELS; MODELING NONLINEAR SYSTEM; NON-LINEAR PDES; NONLINEAR ODES;

EID: 79955521845     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.02.014     Document Type: Article
Times cited : (46)

References (31)
  • 3
    • 79952186660 scopus 로고    scopus 로고
    • Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives
    • N. Bellomo, and B. Carbonaro Toward a mathematical theory of living systems focusing on developmental biology and evolution: a review and perspectives Phys. Life Rev. 8 1 2011 1 18
    • (2011) Phys. Life Rev. , vol.8 , Issue.1 , pp. 1-18
    • Bellomo, N.1    Carbonaro, B.2
  • 4
    • 33746069282 scopus 로고    scopus 로고
    • Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems
    • DOI 10.1142/S0218202506001443
    • N. Bellomo, and G. Forni Looking for new paradigms towards a biologicalmathematical theory of complex multicellular systems Math. Models Methods Appl. Sci. 16 2006 1001 1029 (Pubitemid 44076433)
    • (2006) Mathematical Models and Methods in Applied Sciences , vol.16 , Issue.7 , pp. 1001-1029
    • Bellomo, N.1    Forni, G.2
  • 5
    • 44349107599 scopus 로고    scopus 로고
    • On the foundations of cancer modelling: Selected topics, speculations, and perspectives
    • DOI 10.1142/S0218202508002796, PII S0218202508002796
    • N. Bellomo, Ph.K. Maini, and N.L. Martin On the foundations of cancer modelling: selected topics, speculations and perspectives Math. Models Methods Appl. Sci. 18 2008 593 646 (Pubitemid 351730142)
    • (2008) Mathematical Models and Methods in Applied Sciences , vol.18 , Issue.4 , pp. 593-646
    • Bellomo, N.1    Li, N.K.2    Maini, P.K.3
  • 6
    • 42149122635 scopus 로고    scopus 로고
    • Links between microscopic and macroscopic descriptions
    • Multiscale Problems in the Life Sciences. from Microscopic to Macroscopic
    • M. Lachowicz Links between microscopic and macroscopic descriptions V. Capasso, M. Lachowicz, Multiscale Problems in the Life Sciences. From Microscopic to Macroscopic Lecture Notes in Mathematics 2008 Springer 201 268
    • (2008) Lecture Notes in Mathematics , pp. 201-268
    • Lachowicz, M.1
  • 7
    • 77957755467 scopus 로고    scopus 로고
    • Microscopic, mesoscopic and macroscopic descriptions of complex systems
    • M. Lachowicz Microscopic, mesoscopic and macroscopic descriptions of complex systems Probab. Eng. Mech. 26 1 2011 54 60
    • (2011) Probab. Eng. Mech. , vol.26 , Issue.1 , pp. 54-60
    • Lachowicz, M.1
  • 9
    • 67249121364 scopus 로고    scopus 로고
    • Limit theorems for individuals-based models in economics and finance
    • D. Remenik Limit theorems for individuals-based models in economics and finance Stochastic Process. Appl. 119 2009 2401 2435
    • (2009) Stochastic Process. Appl. , vol.119 , pp. 2401-2435
    • Remenik, D.1
  • 11
    • 18944381178 scopus 로고    scopus 로고
    • On bilinear kinetic equations. between micro and macro descriptions of biological populations
    • M. Lachowicz On bilinear kinetic equations. Between micro and macro descriptions of biological populations Banach Center Publ. 63 2004 217 230
    • (2004) Banach Center Publ. , vol.63 , pp. 217-230
    • Lachowicz, M.1
  • 12
    • 18944388598 scopus 로고    scopus 로고
    • General population systems. Macroscopic limit of a class of stochastic semigroups
    • DOI 10.1016/j.jmaa.2005.03.020, PII S0022247X0500209X
    • M. Lachowicz General population systems. Macroscopic limit of a class of stochastic semigroups J. Math. Anal. Appl. 307 2005 585 605 (Pubitemid 40707091)
    • (2005) Journal of Mathematical Analysis and Applications , vol.307 , Issue.2 , pp. 585-605
    • Lachowicz, M.1
  • 13
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • DOI 10.1142/S0218202505000935
    • M. Lachowicz Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours Math. Models Methods Appl. Sci. 15 2005 1667 1683 (Pubitemid 41551042)
    • (2005) Mathematical Models and Methods in Applied Sciences , vol.15 , Issue.11 , pp. 1667-1683
    • Lachowicz, M.1
  • 14
    • 42149090450 scopus 로고    scopus 로고
    • Rescaling stochastic processes: Asymptotic
    • Multiscale Problems in the Life Sciences. from Microscopic to Macroscopic
    • V. Capasso, and D. Morale Rescaling stochastic processes: asymptotic V. Capasso, M. Lachowicz, Multiscale Problems in the Life Sciences. From Microscopic to Macroscopic Lecture Notes in Mathematics 2008 Springer 91 146
    • (2008) Lecture Notes in Mathematics , pp. 91-146
    • Capasso, V.1    Morale, D.2
  • 15
    • 70449515071 scopus 로고    scopus 로고
    • Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions
    • V. Capasso, and D. Morale Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions Stoch. Anal. Appl. 27 2009 574 603
    • (2009) Stoch. Anal. Appl. , vol.27 , pp. 574-603
    • Capasso, V.1    Morale, D.2
  • 16
    • 33645741606 scopus 로고    scopus 로고
    • Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models
    • N. Champagnat, R. Ferrire, and S. Mlard Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models Theor. Popul. Biol. 69 2006 297 321
    • (2006) Theor. Popul. Biol. , vol.69 , pp. 297-321
    • Champagnat, N.1    Ferrire, R.2    Mlard, S.3
  • 17
    • 55849103220 scopus 로고    scopus 로고
    • From individual stochastic processes to macroscopic models in adaptive evolution
    • N. Champagnat, R. Ferrire, and S. Mlard From individual stochastic processes to macroscopic models in adaptive evolution Stoch. Models 24 2008 2 44 2006, pp. 297321
    • (2008) Stoch. Models , vol.24 , pp. 2-44
    • Champagnat, N.1    Ferrire, R.2    Mlard, S.3
  • 19
    • 13844298300 scopus 로고    scopus 로고
    • An interacting particle system modelling aggregation behavior: From individuals to populations
    • DOI 10.1007/s00285-004-0279-1
    • D. Morale, V. Capasso, and K. Oelschlger An interacting particle system modelling aggregation behaviour: from individuals to populations J. Math. Biol. 50 2005 49 66 (Pubitemid 40240753)
    • (2005) Journal of Mathematical Biology , vol.50 , Issue.1 , pp. 49-66
    • Morale, D.1    Capasso, V.2    Oelschlager, K.3
  • 20
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
    • DOI 10.1137/S0036139998342065, PII S0036139998342065
    • A. Stevens The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems SIAM J. Appl. Math. 61 2000 183 212 (Pubitemid 32286522)
    • (2000) SIAM Journal on Applied Mathematics , vol.61 , Issue.1 , pp. 183-212
    • Stevens, A.1
  • 21
    • 3943098680 scopus 로고    scopus 로고
    • Stochastic interacting particle systems and nonlinear kinetic equations
    • DOI 10.1214/aoap/1060202829
    • A. Eibeck, and W. Wagner Stochastic interacting particle systems and nonlinear kinetic equations Ann. Appl. Probab. 13 2003 845 889 (Pubitemid 39050992)
    • (2003) Annals of Applied Probability , vol.13 , Issue.3 , pp. 845-889
    • Eibeck, A.1    Wagner, W.2
  • 22
    • 21444453847 scopus 로고    scopus 로고
    • A functional law of large numbers for Boltzmann type stochastic particle systems
    • W. Wagner A functional law of large numbers for Boltzmann type stochastic particle systems Stoch. Anal. Appl. 14 1996 591 636
    • (1996) Stoch. Anal. Appl. , vol.14 , pp. 591-636
    • Wagner, W.1
  • 25
    • 0344211073 scopus 로고    scopus 로고
    • An integrodifferential model for orientational distribution of F-actin in cells
    • E. Geigant, K. Ladizhansky, and A. Mogilner An integrodifferential model for orientational distribution of F-actin in cells SIAM J. Appl. Math. 59 1998 787 809
    • (1998) SIAM J. Appl. Math. , vol.59 , pp. 787-809
    • Geigant, E.1    Ladizhansky, K.2    Mogilner, A.3
  • 26
    • 0026932946 scopus 로고
    • On the distribution of dominance in populations of social organisms
    • E. Jger, and L. Segel On the distribution of dominance in a population of interacting anonymous organisms SIAM J. Appl. Math. 52 1992 1442 1468 (Pubitemid 23589677)
    • (1992) SIAM Journal on Applied Mathematics , vol.52 , Issue.5 , pp. 1442-1468
    • Jager Eva1    Segel Lee, A.2
  • 27
    • 0347081772 scopus 로고    scopus 로고
    • Nonlocal bilinear equations. Equilibrium solutions and diffusive limit
    • M. Lachowicz, and D. Wrzosek Nonlocal bilinear equations. Equilibrium solutions and diffusive limit Math. Models Methods Appl. Sci. 11 2001 1375 1390
    • (2001) Math. Models Methods Appl. Sci. , vol.11 , pp. 1375-1390
    • Lachowicz, M.1    Wrzosek, D.2
  • 28
    • 0024731820 scopus 로고
    • The quasi-steady-state assumption: A case study in perturbation
    • L.A. Segel, and M. Slemrod The quasi-steady-state assumption: a case study in perturbation SIAM Rev. 31 1989 446 477
    • (1989) SIAM Rev. , vol.31 , pp. 446-477
    • Segel, L.A.1    Slemrod, M.2
  • 30
    • 33747088162 scopus 로고    scopus 로고
    • Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy
    • DOI 10.1142/S0218202506001571, PII S0218202506001571
    • A. d'Onofrio Tumor-immune system interaction modeling the tumor-stimulated proliferation of effectors and immunotherapy Math. Models Methods Appl. Sci. 16 8 2006 1375 1401 (Pubitemid 44221742)
    • (2006) Mathematical Models and Methods in Applied Sciences , vol.16 , Issue.8 , pp. 1375-1401
    • D'Onofrio, A.1
  • 31
    • 38849187163 scopus 로고    scopus 로고
    • Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy
    • A. d'Onofrio Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy Math. Comput. Modelling 46 2008 614 637
    • (2008) Math. Comput. Modelling , vol.46 , pp. 614-637
    • D'Onofrio, A.1


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