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2014 | 24 | 3 | 635-646
Tytuł artykułu

An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results.
Rocznik
Tom
24
Numer
3
Strony
635-646
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-05-31
poprawiono
2013-11-15
poprawiono
2014-03-08
Twórcy
autor
  • Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai Shangdong 264209, PR China
autor
  • Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai Shangdong 264209, PR China
autor
  • Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai Shangdong 264209, PR China
Bibliografia
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  • Dimitrov, D. and Kojouharov, H. (2007). Stability-preserving finite-difference methods for general multi-dimensional autonomous dynamical systems, International Journal of Numerical Analysis and Modeling 4(2): 280-290.
  • Dimitrov, D. and Kojouharov, H. (2008). Nonstandard finite difference methods for predator-prey models with general functional response, Mathematics and Computers in Simulation 78(1): 1-11.
  • Ding, D., Ma, Q. and Ding, X. (2013). A non-standard finite difference scheme for an epidemic model with vaccination, Journal of Difference Equations and Applications 19(2): 179-190.
  • Dumont, Y. and Lubuma, J.M.-S. (2005). Non-standard finite-difference methods for vibro-impact problems, Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences 461(2058): 1927-1950.
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  • Kouche, M. and Ainseba, B. (2010). A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation, International Journal of Applied Mathematics and Computer Science 20(3): 601-612, DOI: 10.2478/v10006-010-0045-z.
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  • Mickens, R. (2000). Advances in the Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore.
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  • Mickens, R. (2005). Dynamic consistency: A fundamental principle for constructing nonstandard finite difference schemes for differential equations, Journal of Difference Equations and Applications 11(7): 645-653.
  • Moghadas, S., Alexander, M. and Corbett, B.D.and Gumel, A. (2003). A positivity preserving Mickens-type discretization of an epidemic model, Journal of Difference Equations and Applications 9(11): 1037-1051.
  • Moghadas, S. and Gumel, A. (2003). A mathematical study of a model for childhood diseases with non-permanent immunity, Journal of Computational and Applied Mathematics 157(2): 347-363.
  • Muroya, Y., Nakata, Y., Izzo, G. and Vecchio, A. (2011). Permanence and global stability of a class of discrete epidemic models, Nonlinear Analysis: Real World Applications 12(4): 2105-2117.
  • Obaid, H., Ouifki, R. and Patidar, K.C. (2013). An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection, International Journal of Applied Mathematics and Computer Science 23(2): 357-372, DOI: 10.2478/amcs-2013-0027.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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