Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 7, Number 5, 2012
Immunology
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Page(s) | 7 - 23 | |
DOI | https://doi.org/10.1051/mmnp/20127503 | |
Published online | 17 October 2012 |
- A.S. Ackleh, H.T. Banks, K. Deng. A finite difference approximation for a coupled system of nonlinear size-structured populations. Nonlinear Analysis, 50 (2002), 727–748. [Google Scholar]
- A.S. Ackleh, K. Ito. An implicit finite-difference scheme for the nonlinear size-structured population model. Numer. Funct. Anal. Optim. 18 (1997), 65–884. [CrossRef] [MathSciNet] [Google Scholar]
- A.S. Ackleh, K. Deng. A monotone approximation for the nonautonomous size-structured population model. Quart. Appl. Math., 57 (1999), 261–267. [MathSciNet] [Google Scholar]
- O. Angulo, J.C. López-Marcos, Numerical integration of fully nonlinear size-structured population models. Applied Numerical Mathematics, 50 (2004), 291–327. [CrossRef] [MathSciNet] [Google Scholar]
- H.T. Banks. A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering, CRC Press/Taylor and Frances Publishing, Boca Raton, FL, June, 2012, (258 pages). [Google Scholar]
- H.T. Banks, K.L. Bihari. Modelling and estimating uncertainty in parameter estimation. Inverse Problems, 17 (2001), 95–111. [CrossRef] [MathSciNet] [Google Scholar]
- H.T. Banks, V.A. Bokil, S. Hu, A.K. Dhar, R.A. Bullis, C.L. Browdy, F.C.T. Allnutt. Modeling shrimp biomass and viral infection for production of biological countermeasures CRSC-TR05-45, NCSU, December, 2005 ; Mathematical Biosciences and Engineering, 3 (2006), 635–660. [Google Scholar]
- H.T. Banks, L.W. Botsford, F. Kappel, C. Wang. Modeling and estimation in size structured population models. LCDS-CCS Report 87-13, Brown University ; Proceedings 2nd Course on Mathematical Ecology, (Trieste, December 8-12, 1986) World Press, Singapore, 1988, 521–541. [Google Scholar]
- H.T. Banks, F. Charles, M. Doumic, K.L. Sutton, W.C. Thompson. Label structured cell proliferation models. Appl. Math. Letters, 23 (2010), 1412–1415. [CrossRef] [MathSciNet] [Google Scholar]
- H.T. Banks, J.L. Davis. A comparison of approximation methods for the estimation of probability distributions on parameters. CRSC-TR05-38, October, 2005 ; Applied Numerical Mathematics, 57 (2007), 753–777. [Google Scholar]
- H.T. Banks, J.L. Davis. Quantifying uncertainty in the estimation of probability distributions. CRSC-TR07-21, December, 2007 ; Math. Biosci. Engr., 5 (2008), 647–667. [Google Scholar]
- H.T. Banks, J.L. Davis, S.L. Ernstberger, S. Hu, E. Artimovich, A.K. Dhar, C.L. Browdy. A comparison of probabilistic and stochastic differential equations in modeling growth uncertainty and variability. CRSC-TR08-03, NCSU, February, 2008 ; Journal of Biological Dynamics, 3 (2009), 130–148. [Google Scholar]
- H.T. Banks, J.L. Davis, S.L. Ernstberger, S. Hu, E. Artimovich, A.K. Dhar. Experimental design and estimation of growth rate distributions in size-structured shrimp populations. CRSC-TR08-20, NCSU, November, 2008 ; Inverse Problems, 25 (2009), 095003(28pp). [Google Scholar]
- H.T. Banks, J.L. Davis, S. Hu. A computational comparison of alternatives to including uncertainty in structured population models. CRSC-TR09-14, June, 2009 ; Three Decades of Progress in Systems and Control, X. Hu, U. Jonsson, B. Wahlberg, B. Ghosh (Eds.), Springer, 2010, 19–33. [Google Scholar]
- H.T. Banks, B.G. Fitzpatrick. Estimation of growth rate distributions in size structured population models. Quarterly of Applied Mathematics, 49 (1991), 215–235. [Google Scholar]
- H.T. Banks, B.G. Fitzpatrick, L.K. Potter, Y. Zhang. Estimation of probability distributions for individual parameters using aggregate population data. CRSC-TR98-6, NCSU, January, 1998 ; Stochastic Analysis, Control, Optimization and Applications, (Edited by W. McEneaney, G. Yin and Q. Zhang), Birkhauser, Boston, 1998, 353–371. [Google Scholar]
- H.T. Banks, S. Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations. CRSC-TR11-02, NCSU, January, 2011 ; Mathematical Bioscience and Engineering, 9 (2012), 1–25. [Google Scholar]
- H.T. Banks, F. Kappel. Transformation semigroups and L1-approximation for size- structured population models. Semigroup Forum, 38 (1989), 141–155. [CrossRef] [MathSciNet] [Google Scholar]
- H.T. Banks, F. Kappel, C. Wang. Weak solutions and differentiability for size-structured population models. International Series of Numerical Mathematics, 100 (1991), 35–50. [Google Scholar]
- H.T. Banks, G.A. Pinter. A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue, CRSC-TR04-03, January, 2004 ; SIAM J. Multiscale Modeling and Simulation, 3 (2005), 395–412. [CrossRef] [Google Scholar]
- H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, M. Doumic, T. Schenkel, J. Argilaguet, S. Giest, C. Peligero, A. Meyerhans. A new model for the estimation of cell proliferation dynamics using CFSE data. Center for Research in Scientific Computation Technical Report CRSC-TR11-05, NCSU, July, 2011 ; J. Immunological Methods, 373 (2011), 143–160. [Google Scholar]
- H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, D. Roose, T. Schenkel, A. Meyerhans. Estimation of cell proliferation dynamics using CFSE data, CRSC-TR09-17, NCSU, August, 2009 ; Bull. Math. Biol. 70 (2011), 116–150; doi :10.1007/s11538-010-9524-5. [Google Scholar]
- H.T. Banks, W.C. Thompson. Mathematical models of dividing cell populations : Application to CFSE data. CRSC-TR12-10, N. C. State University, Raleigh, NC, April, 2012 ; Journal on Mathematical Modelling of Natural Phenomena, to appear. [Google Scholar]
- H.T. Banks, W.C. Thompson. A division-dependent compartmental model with cyton and intracellular label dynamics. CRSC-TR12-12, N. C. State University, Raleigh, NC, May, 2012 ; Intl. J. of Pure and Applied Math., 77 (2012), 119–147. [Google Scholar]
- H.T. Banks, W.C. Thompson, C. Peligero, S. Giest, J. Argilaguet, A. Meyerhans. A compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays, CRSC-TR12-03, NCSU, January, 2012 ; Math. Biosci. Engr., to appear. [Google Scholar]
- H.T. Banks, H.T. Tran, D.E. Woodward. Estimation of variable coefficients in the Fokker-Planck equations using moving node finite elements. SIAM J. Numer. Anal., 30 (1993), 1574–1602. [CrossRef] [MathSciNet] [Google Scholar]
- G.I. Bell, E.C. Anderson. Cell growth and division I. a mathematical model with applications to cell volume distributions in mammalian suspension cultures. Biophysical Journal, 7 (1967), 329–351. [CrossRef] [PubMed] [Google Scholar]
- A. Calsina, J. Saldana. A model of physiologically structured population dynamics with a nonlinear individual growth rate. Journal of Mathematical Biology, 33 (1995), 335–364. [Google Scholar]
- G. Casella, R.L. Berger. Statistical Inference. Duxbury, California, 2002. [Google Scholar]
- F.L. Castille, T.M. Samocha, A.L. Lawrence, H. He, P. Frelier, F. Jaenike. Variability in growth and survival of early postlarval shrimp (Penaeus vannamei Boone 1931) Aquaculture, 113 (1993), 65–81. [CrossRef] [Google Scholar]
- J. Chu, A. Ducrot, P. Magal, S. Ruan. Hopf bifurcation in a size-structured population dynamic model with random growth. J. Differential Equations, 247 (2009), 956–1000. [CrossRef] [MathSciNet] [Google Scholar]
- J.M. Cushing. An Introduction to Structured Population Dynamics. CMB-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA, 1998. [Google Scholar]
- T.C. Gard. Introduction to Stochastic Differential Equations. Marcel Dekker, New York, 1988. [Google Scholar]
- C.W. Gardiner. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer-Verlag, Berlin, 1983. [Google Scholar]
- M. Gyllenberg, G.F. Webb. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol., 28 (1990), 671–694. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- G.W. Harrison. Numerical solution of the Fokker-Planck equation using moving finite elements. Numerical Methods for Partial Differential Equations, 4 (1988), 219–232. [CrossRef] [Google Scholar]
- J. Hasenauer, D. Schittler, F. Allgöer. A computational model for proliferation dynamics of division- and label-structured populations. February, 2012, preprint. [Google Scholar]
- J. Hasenauer, S. Waldherr, M. Doszczak, P. Scheurich, N. Radde, F. Allgöer. Analysis of heterogeneous cell populations : a density-based modeling and identification framework. J. Process Control, 21 (2011), 1417–1425. [CrossRef] [Google Scholar]
- K. Huang. Statistical Mechanics. J. Wiley & Sons, New York, NY, 1963. [Google Scholar]
- M. Iannelli. Mathematical Theory of Age-Structured Population Dynamics. Applied Math. Monographs, CNR, Giardini Editori e Stampatori, Pisa, 1995. [Google Scholar]
- M. Kimura. Process leading to quasi-fixation of genes in natural populations due to random fluctuation of selection intensities. Genetics, 39 (1954), 280–295. [PubMed] [Google Scholar]
- F. Klebaner. Introduction to Stochastic Calculus with Applications. 2nd ed., Imperial College Press, London, 2006. [Google Scholar]
- I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer, New York, 1991. [Google Scholar]
- T. Luzyanina, D. Roose, G. Bocharov. Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data. J. Math. Biol., 59 (2009), 581–603. [CrossRef] [MathSciNet] [Google Scholar]
- T. Luzyanina, M. Mrusek, J.T. Edwards, D. Roose, S. Ehl, G. Bocharov. Computational analysis of CFSE proliferation assay. J. Math. Biol., 54 (2007), 57–89. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- T. Luzyanina, D. Roose, T. Schenkel, M. Sester, S. Ehl, A. Meyerhans, G. Bocharov. Numerical modelling of label-structured cell population growth using CFSE distribution data. Theoretical Biology and Medical Modelling, 4(2007), Published Online. [Google Scholar]
- A.G. McKendrick. Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society, 44 (1926), 98–130. [Google Scholar]
- J.A.J. Metz, E.O. Diekmann, The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics, Vol. 68, Springer, Heidelberg, 1986. [Google Scholar]
- J.E. Moyal. Stochastic processes and statistical physics. Journal of the Royal Statistical Society. Series B (Methodological), 11 (1949), 150–210. [MathSciNet] [Google Scholar]
- Yu. V. Prohorov. Convergence of random processes and limit theorems in probability theory. Theor. Prob. Appl., 1 (1956), 157–214. [Google Scholar]
- B. Oksendal. Stochastic Differentail Equations. 5th edition, Springer, Berlin, 2000. [Google Scholar]
- A. Okubo. Diffusion and Ecological Problems : Mathematical Models. Biomathematics, 10 (1980), Springer-Verlag, Berlin. [Google Scholar]
- G. Oster, Y. Takahashi. Models for age-specific interactions in a periodic environment. Ecological Monographs, 44 (1974), 483–501. [CrossRef] [Google Scholar]
- B. Perthame. Transport Equations in Biology. Birkhauser Verlag, Basel, 2007. [Google Scholar]
- R. Rudnicki. Models of population dynamics and genetics. From Genetics To Mathematics, (edited by M. Lachowicz and J. Miekisz), World Scientific, Singapore, 2009, 103–148. [Google Scholar]
- H. Risken. The Fokker-Planck Equation : Methods of Solution and Applications. Springer, New York, 1996. [Google Scholar]
- D. Schittler, J. Hasenauer, F. Allgöer. A generalized population model for cell proliferation : Integrating division numbers and label dynamics. Proceedings of Eighth International Workshop on Computational Systems Biology (WCSB 2011), June 2011, Zurich, Switzerland, 165–168. [Google Scholar]
- D. Schittler, J. Hasenauer, F. Allgöer. A model for proliferating cell populations that accounts for cell types. Proc. of 9th International Workshop on Computational Systems Biology, 2012, 84–87. [Google Scholar]
- J. Sinko, W. Streifer. A new model for age-size structure of a population. Ecology, 48 (1967), 910–918. [CrossRef] [Google Scholar]
- T.T. Soong. Random Differential Equations in Science and Engineering. Academic Press, New York and London, 1973. [Google Scholar]
- T.T. Soong, S.N. Chuang. Solutions of a class of random differential equations. SIAM J. Appl. Math., 24 (1973), 449–459. [CrossRef] [Google Scholar]
- W.C. Thompson. Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays. Ph.D. Dissertation, North Carolina State University, December, 2011. [Google Scholar]
- H. Von Foerster. Some remarks on changing populations. The Kinetics of Cellular Proliferation, F. Stohlman, Jr. (ed.), Grune and Stratton, New York, 1959. [Google Scholar]
- G.F. Webb. Theory of Nonlinear Age-dependent Population Dynamics. Marcel Dekker, New York, 1985. [Google Scholar]
- A.Y. Weiße, R.H. Middleton, W. Huisinga. Quantifying uncertainty, variability and likelihood for ordinary differential equation models. BMC Syst. Bio., 4 (144), 2010. [Google Scholar]
- G.H. Weiss Equation for the age structure of growing populations. Bull. Math. Biophy., 30 (1968), 427–435. [CrossRef] [Google Scholar]
- http://en.wikipedia.org/wiki/Probability_density_function. [Google Scholar]
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