Mathematical Biosciences and Engineering (MBE)

Nonlinear stochastic Markov processes and modeling uncertainty in populations
Pages: 1 - 25, Issue 1, January 2012

doi:10.3934/mbe.2012.9.1      Abstract        References        Full text (433.9K)           Related Articles

H.Thomas Banks - Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212, United States (email)
Shuhua Hu - Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212, United States (email)

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2 L. J. S. Allen, "An Introduction to Stochastic Processes with Applications to Biology," Second edition, CRC Press, Boca Raton, FL, 2011.       
3 P. Bai, H. T. Banks, S. Dediu, A. Y. Govan, M. Last, A. Loyd, H. K. Nguyen, M. S. Olufsen, G. Rempala and B. D. Slenning, Stochastic and deterministic models for agricultural production networks, Math. Biosci. and Engr., 4 (2007), 373-402.       
4 H. T. Banks and K. L. Bihari, Modelling and estimating uncertainty in parameter estimation, Inverse Problems, 17 (2001), 95-111.       
5 H. T. Banks, V. A. Bokil, S. Hu, A. K. Dhar, R. A. Bullis, C. L. Browdy and F. C. T. Allnutt, Modeling shrimp biomass and viral infection for production of biological countermeasures, Mathematical Biosciences and Engineering, 3 (2006), 635-660.       
6 H. T. Banks, D. M. Bortz, G. A. Pinter and L. K. Potter, Modeling and imaging techniques with potential for application in bioterrorism, in "Bioterrorism" (eds. H. T. Banks and C. Castillo-Chavez), Frontiers in Applied Math., 28, SIAM, Philadelphia, PA, (2003), 129-154.       
7 H. T. Banks, L. W. Botsford, F. Kappel and C. Wang, Modeling and estimation in size structured population models, in "Mathematical Ecology" (Trieste, 1986), World Sci. Publ., Teaneck, NJ, (1988), 521-541.       
8 H. T. Banks and J. L. Davis, Quantifying uncertainty in the estimation of probability distributions, Math. Biosci. Engr., 5 (2008), 647-667.       
9 H. T. Banks, J. L. Davis, S. L. Ernstberger, S. Hu, E. Artimovich, A. K. Dhar and C. L. Browdy, A comparison of probabilistic and stochastic formulations in modeling growth uncertainty and variability, Journal of Biological Dynamics, 3 (2009), 130-148.       
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18 H. T. Banks, K. L. Sutton, W. C. Thompson, G. Bocharov, M. Doumic, T. Schenkel, J. Argilaguet, S. Giest, C. Peligero and A. Meyerhans, A new model for the estimation of cell proliferation dynamics using CFSE data, J. Immunological Methods, submitted.
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33 T. T. Soong, "Random Differential Equations in Science and Engineering," Mathematics in Science and Engineering, Vol. 103, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973.       

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