2011, 8(2): 263-277. doi: 10.3934/mbe.2011.8.263

Modeling and simulation of some cell dispersion problems by a nonparametric method

1. 

ICAM, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany, Germany

Received  February 2010 Revised  December 2010 Published  April 2011

Starting from the classical descriptions of cell motion we propose some ways to enhance the realism of modeling and to account for interesting features like allowing for a random switching between biased and unbiased motion or avoiding a set of obstacles. For this complex behavior of the cell population we propose new models and also provide a way to numerically assess the macroscopic densities of interest upon using a nonparametric estimation technique. Up to our knowledge, this is the only method able to numerically handle the entire complexity of such settings.
Citation: Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method. Mathematical Biosciences & Engineering, 2011, 8 (2) : 263-277. doi: 10.3934/mbe.2011.8.263
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International Journal of Biomathematics and Biostatistics, 1 (2010), 109-128. Google Scholar

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C. Surulescu and N. Surulescu, On two approahes to a multiscale system modeling bacterial chemotaxis,, preprint IANS, ().   Google Scholar

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show all references

References:
[1]

Journal of Mathematical Biology, 9 (1980), 147-177. doi: 10.1007/BF00275919.  Google Scholar

[2]

Springer, 2007.  Google Scholar

[3]

Annals of the Institute of Statistical Mathematics, 18 (1966), 179-189. doi: 10.1007/BF02869528.  Google Scholar

[4]

Mathematical Models and Methods in the Applied Sciences, 16 (2006), 1173-1197. doi: 10.1142/S0218202506001509.  Google Scholar

[5]

Monatshefte für Mathematik, 142 (2004), 123-141.  Google Scholar

[6]

Journal of Mathematical Biology, 51 (2005), 527-556. doi: 10.1007/s00285-005-0317-7.  Google Scholar

[7]

Physical Review Letters, 81 (1998), 3038-3041. doi: 10.1103/PhysRevLett.81.3038.  Google Scholar

[8]

Publications de l'Institut Statistique de l'Université de Paris, 22 (1977), 1-23.  Google Scholar

[9]

John Wiley, New York 1985.  Google Scholar

[10]

Test, 6 (1997), 223-320. doi: 10.1007/BF02564701.  Google Scholar

[11]

Multiscale Modeling and Simulation, 3 (2005), 362-394. doi: 10.1137/040603565.  Google Scholar

[12]

Journal of Mathematical Biology, 50 (2005), 189-207. doi: 10.1007/s00285-004-0286-2.  Google Scholar

[13]

Physics Letters A, 316 (2003), 190-195. doi: 10.1016/j.physleta.2003.07.004.  Google Scholar

[14]

Habilitation Thesis, University of Tübingen, 2001. Google Scholar

[15]

Mathematical Models and Methods in the Applied Sciences, 12 (2002), 1-28. doi: 10.1142/S0218202502002008.  Google Scholar

[16]

European Journal of Applied Mathematics, 14 (2003), 613-636. doi: 10.1017/S0956792503005291.  Google Scholar

[17]

SIAM Journal of Applied Mathematics, 61 (2000), 751-775. doi: 10.1137/S0036139999358167.  Google Scholar

[18]

preprint IANS, University of Stuttgart, 2010, submitted. Google Scholar

[19]

Journal of Multivariate Analysis, 42 (1992), 245-266. doi: 10.1016/0047-259X(92)90046-I.  Google Scholar

[20]

Springer, 2000.  Google Scholar

[21]

Wiley, 2000. doi: 10.1016/0167-7152(88)90050-8.  Google Scholar

[22]

Statistics and Probability Letters, 7 (1988), 195-199. doi: 10.1214/aos/1176348653.  Google Scholar

[23]

Annals of Statistics, 20 (1992), 712-736. doi: 10.1007/BF00277392.  Google Scholar

[24]

preprint, TU Vienna, 2004. doi: 10.1137/S0036139900382772.  Google Scholar

[25]

Journal of Mathematical Biology, 26 (1988), 263-298.  Google Scholar

[26]

SIAM Journal of Applied Mathematics, 62 (2002), 1222-1250.  Google Scholar

[27]

Cambridge University Press, 1999.  Google Scholar

[28]

John Wiley & Sons, 1992.  Google Scholar

[29]

Chapman & Hall, 1986.  Google Scholar

[30]

Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 28 (1974), 305-315.  Google Scholar

[31]

C. Surulescu and N. Surulescu, A nonparametric approach to cell dispersal,, preprint IANS 14/2007, ().   Google Scholar

[32]

International Journal of Biomathematics and Biostatistics, 1 (2010), 109-128. Google Scholar

[33]

C. Surulescu and N. Surulescu, On two approahes to a multiscale system modeling bacterial chemotaxis,, preprint IANS, ().   Google Scholar

[34]

PLoS ONE, 3 (2008), e2648. doi: 10.1371/journal.pone.0002648.  Google Scholar

[35]

Physica A: Statistical Mechanics and its Applications, 293 (2001), 549-558. Google Scholar

[36]

Journal of Multivariate Analysis, 39 (1991), 324-347. doi: 10.1016/0047-259X(91)90105-B.  Google Scholar

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