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A nonstandard finite difference scheme for a multi-group epidemic model with time delay

Authors :
Jinhu Xu
Yan Geng
Source :
Advances in Difference Equations, Vol 2017, Iss 1, Pp 1-11 (2017)
Publication Year :
2017
Publisher :
SpringerOpen, 2017.

Abstract

Abstract In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stability are identical in case of both the discrete and the corresponding continuous models. Specifically, if R 0 ≤ 1 $\mathfrak{R}_{0}\leq1$ , then the disease-free equilibrium P 0 $P_{0}$ is globally asymptotically stable; if R 0 > 1 $\mathfrak{R}_{0}>1$ , then the infection equilibrium P ∗ $P_{*}$ is globally asymptotically stable. The results imply that the discretization scheme can efficiently preserve the global dynamics of the original continuous model.

Details

Language :
English
ISSN :
16871847
Volume :
2017
Issue :
1
Database :
Directory of Open Access Journals
Journal :
Advances in Difference Equations
Publication Type :
Academic Journal
Accession number :
edsdoj.1f966cec19b4eb19250db821cca26cb
Document Type :
article
Full Text :
https://doi.org/10.1186/s13662-017-1415-8