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Original Articles

Numerical integration of population models satisfying conservation laws: NSFD methods

Pages 427-436 | Received 02 Apr 2007, Published online: 12 Nov 2007

References

  • Edelstein-Keshet , L. 1988 . Mathematical Models in Biology , New York : McGraw-Hill .
  • Strogatz , S. H. 1994 . Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering , New York : Addison-Wesley .
  • Nowak , M. A. and May , R. M. 2000 . Virus Dynamics , New York : Oxford University Press .
  • Thieme , H. R. 2003 . Mathematics in Population Biology , Princeton, NJ : Princeton University Press .
  • Zwillinger , D. 1989 . Handbook of Differential Equations , New York : Academic Press .
  • Mickens , R. E. 1994 . Nonstandard Finite Difference Models of Differential Equations , Singapore : World Scientific .
  • Jain , M. K. 1984 . Numerical Solution of Differential Equations , New York : John Wiley/Halsted .
  • Mickens , R. E. 2000 . Applications of Nonstandard Finite Difference Schemes , Edited by: Mickens , R. E. Singapore : World Scientific .
  • Mickens , R. E. 2005 . Dynamic consistency: A fundamental principle for constructing NSFD schemes for differential equations . Journal of Difference Equations and Applications , 11 : 645 – 653 .
  • Mickens , R. E. 2007 . Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition . Numerical Methods for Partial Differential Equations , 23 : 672 – 691 .
  • Mickens , R. E. 2005 . Advances in the Applications of Nonstandard Finite Difference Schemes , Singapore : World Scientific .
  • Brauer , F. and Castillo-Chávez , C. 2001 . Mathematical Models in Population Biology and Epidemiology , Berlin : Springer-Verlag . section 7.4
  • Murray , J. D. 1989 . Mathematical Biology , Berlin : Springer-Verlag .
  • Diekmann , O. and Heesterbeek , J. A.P. 2000 . Mathematical Epidemiology of Infectious Diseases , New York : John Wiley .
  • Liu , W.-M. , Levin , S. A. and Iwasa , Y. 1986 . Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models . Journal of Mathematical Biology , 23 : 187 – 204 .
  • Liu , W.-M. , Hethcote , H. W. and Levin , S. A. 1987 . Dynamical behavior of epidemiological models with nonlinear incidence rates . Journal of Mathematical Biology , 25 : 359 – 380 .

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