<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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</p></abstract>

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

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

Department of Mathematics Harbin Institute of Technology (Weihai), Weihai Shangdong 264209, PR China

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with...

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

Publié en ligne: 25 sept. 2014

Pages: 635 - 646

Reçu: 31 mai 2013

DOI: https://doi.org/10.2478/amcs-2014-0046

Mots clés
nonstandard finite differences, unconditional positivity, stability, Lyapunov function

© by Deqiong Ding

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Publié en ligne: 25 sept. 2014

Pages: 635 - 646

Reçu: 31 mai 2013

DOI: https://doi.org/10.2478/amcs-2014-0046

Mots clésnonstandard finite differences, unconditional positivity, stability, Lyapunov function

© by Deqiong Ding

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
nonstandard finite differences, unconditional positivity, stability, Lyapunov function