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Original Articles

A non-standard finite difference scheme for an epidemic model with vaccination

, &
Pages 179-190 | Received 17 Apr 2011, Accepted 10 Aug 2011, Published online: 29 Sep 2011

References

  • Anderson , R.M. and May , R.M. 1991 . Infectious Diseases of Humans: Dynamics and Control , Oxford and New York : Oxford University Press .
  • Anguelov , R. and Lubuma , J.M.-S. 2001 . Contributions to the mathematics of the nonstandard finite difference method and applications . Numer. Methods Partial Differ. Equ. , 17 : 518 – 543 .
  • Anguelov , R. and Lubuma , J.M.-S. 2003 . Nonstandard finite difference method by nonlocal approximation . Math. Comput. Simul. , 61 : 465 – 475 .
  • Arenas , A.J. , Moraño , J.A. and Cortés , J.C. 2008 . Non-standard numerical method for a mathematical model of RSV epidemiological transmission . Comput. Math. Appl. , 56 : 670 – 678 .
  • Chen , M. and Clemence , D.P. 2006 . Stability properties of a nonstandard finite difference scheme for a hantavirus epidemic model . J. Differ. Equ. Appl. , 12 : 1243 – 1256 .
  • Chen-Charpentier , B.M. , Dimitrov , D.T. and Kojouharov , H.V. 2006 . Combined nonstandard numerical methods for ODEs with polynomial right-hand sides . Math. Comput. Simul. , 73 : 105 – 113 .
  • Chen-Charpentier , B.M. , Dimitrov , D.T. and Kojouharov , H.V. 2007 . Numerical simulation of multi-species biofilms in porous media for different kinetics . Math. Comput. Simul. , 6 : 1846 – 1861 .
  • Chinviriyasit , S. and Chinviriyasit , W. 2010 . Numerical modelling of an SIR epidemic model with diffusion . Appl. Math. Comput. , 216 : 395 – 409 .
  • Dimitrov , D.T. and Kojouharov , H.V. 2005 . Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems . Appl. Math. Lett. , 18 : 769 – 774 .
  • Dimitrov , D.T. and Kojouharov , H.V. 2008 . Nonstandard finite difference methods for predatorCprey models with general functional response . Math. Comput. Simul. , 78 : 1 – 11 .
  • Enatsu , Y. , Nakata , Y. and Muroya , Y. 2010 . Global stability for a class of discrete SIR epidemic models . Math. Biosci. Eng. , 7 : 347 – 361 .
  • Gumel , A.B. 2002 . A competitive numerical method for a chemotherapy model of two HIV subtypes . Appl. Math. Comput. , 131 : 329 – 337 .
  • Jang , S.R.-J. 2007 . On a discrete West Nile epidemic model . Comput. Appl. Math. , 3 : 397 – 414 .
  • Jang , S. and Elaydi , S.N. 2003 . Difference equations from discretization of a continuous epidemic model with immigration of infectives . Can. Appl. Math. Q. , 11 : 93 – 105 .
  • Jansen , H. and Twizell , E.H. 2002 . An unconditionally convergent discretization of the SEIR model . Math. Comput. Simul. , 58 : 147 – 158 .
  • Jódar , L. , Villanueva , R.J. , Arenas , A.J. and González , G.C. 2008 . Nonstandard numerical methods for a mathematical model for influenza disease . Math. Comput. Simul. , 79 : 622 – 633 .
  • Lambert , J.D. 1991 . Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , Chichester : Wiley .
  • Ma , Z. and Li , J. 2009 . Dynamical Modeling and Analysis of Epidemics , Singapore : World Scientific .
  • Ma , Z. , Zhou , Y. , Wang , W. and Jing , Z. 2004 . The Mathematical Modeling and Study of the Dynamics of Infectious Diseases , Beijing : Science Press .
  • Mickens , R.E. 1994 . Nonstandard Finite Difference Model of Differential Equations , Singapore : World Scientific .
  • Mickens , R.E. 2000 . Application of Nonstandard Finite Difference Schemes , Singapore : World Scientific .
  • Mickens , R.E. 2002 . Nonstandard finite difference schemes for differential equations . J. Differ. Equ. Appl. , 8 : 823 – 847 .
  • Mickens , R.E. 2005 . Dynamic consistency: A fundamental principle for constructing nonstandard finite difference schemes for differential equations . J. Differ. Equ. Appl. , 11 : 645 – 653 .
  • Moghadas , S.M. , Alexander , M.E. , Corbett , B.D. and Gumel , A.B. 2003 . A positivity preserving Mickens-type discretization of an epidemic model . J. Differ. Equ. Appl. , 9 : 1037 – 1051 .
  • Muroya , Y. , Nakata , Y. , Izzo , G. and Vecchio , A. 2011 . Permanence and global stability of a class of discrete epidemic models . Nonlinear Anal. Real. , 12 : 2105 – 2117 .
  • Sekiguchi , M. 2009 . Permanence of some discrete epidemic models . Int. J. Biomath. , 2 : 443 – 461 .
  • Sekiguchi , M. 2010 . Permanence of a discrete SIRS epidemic model with time delays . Appl. Math. Lett. , 23 : 1280 – 1285 .
  • Sekiguchi , M. and Ishiwata , E. 2010 . Global dynamics of a discretized SIRS epidemic model with time delay . J. Math. Anal. Appl. , 371 : 195 – 202 .
  • Stuart , A.M. and Humphries , A.R. 1996 . Dynamic System and Numerical Analysis , New York : Cambridge University Press .

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