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R. E. Mickens, “Numerical Integration of Population Models Satisfying Conservation Laws: NSFD Methods,” Journal of Biological Dynamics, Vol. 1, No. 4, 2007, pp. 427-436. doi:10.1080/17513750701605598

has been cited by the following article:

• TITLE: A Nonstandard Finite Difference Scheme for SIS Epidemic Model with Delay: Stability and Bifurcation Analysis

  AUTHORS: Agus Suryanto

  KEYWORDS: SIS Epidemic Model with Delay; Stability; Nonstandard Finite Difference Method; Neimark-Sacker (Hopf) Bifurcation

  JOURNAL NAME: Applied Mathematics, Vol.3 No.6, June 21, 2012

  ABSTRACT: A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the linearized system, we can provide the stable regions in the appropriate parameter plane. It is shown that the conditions for those equilibria to be asymptotically stable are consistent with the continuous model for any size of numerical time-step. Furthermore, we also establish the existence of Neimark-Sacker bifurcation (also called Hopf bifurcation for map) which is controlled by the time delay. The analytical results are confirmed by some numerical simulations.