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

Deqiong Ding; Qiang Ma; Xiaohua Ding

International Journal of Applied Mathematics and Computer Science (2014)

  • Volume: 24, Issue: 3, page 635-646
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Deqiong Ding, Qiang Ma, and Xiaohua Ding. "An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination." International Journal of Applied Mathematics and Computer Science 24.3 (2014): 635-646. <http://eudml.org/doc/271925>.

@article{DeqiongDing2014,
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.},
author = {Deqiong Ding, Qiang Ma, Xiaohua Ding},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonstandard finite differences; unconditional positivity; stability; Lyapunov function},
language = {eng},
number = {3},
pages = {635-646},
title = {An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination},
url = {http://eudml.org/doc/271925},
volume = {24},
year = {2014},
}

TY - JOUR
AU - Deqiong Ding
AU - Qiang Ma
AU - Xiaohua Ding
TI - An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination
JO - International Journal of Applied Mathematics and Computer Science
PY - 2014
VL - 24
IS - 3
SP - 635
EP - 646
AB - 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.
LA - eng
KW - nonstandard finite differences; unconditional positivity; stability; Lyapunov function
UR - http://eudml.org/doc/271925
ER -

References

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