In this paper, we introduced nonstandard finite difference scheme (NSFD) for solving the continuos model with Michaelis-Menten harvesting rate. We have seen that proposed preserve local stability and positivity. Stability analysis of each fixed point discrete time has been proven. Also, numerical comparisons were made between method other methods.

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 positivit...

A definition of nonstandard universe which gets over the limitation to the finite levels of the cumulative hierarchy is proposed. Though necessarily nonwellfounded, nonstandard universes are arranged in strata in the likeness of superstructures and allow a rank function taking linearly ordered values. Nonstandard universes are also constructed which model the whole ZFC theory without regularity...

A ‎nonstandard finite difference (NSFD) scheme has been constructed and analyzed for a mathematical model that describes Lotka–Volterra food web model‎. ‎This new discrete system has the same stability properties as the continuous model and,‎on the whole‎, ‎it preserves‎the same local asymptotic stability properties‎. ‎Linearized stability theory and Schur–Cohn criteria are used for local asymp...

This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the syst...