AN UNCONDITIONALLY POSITIVE AND GLOBAL STABILITY PRESERVING NSFD SCHEME FOR AN EPIDEMIC MODEL WITH VACCINATION

被引：4
|
作者：
Ding, Deqiong [1 ]
Ma, Qiang [1 ]
Ding, Xiaohua [1 ]
机构：
[1] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Shangdong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE | 2014年 / 24卷 / 03期
基金：
中国国家自然科学基金;
关键词：
nonstandard finite differences; unconditional positivity; stability; Lyapunov function; FINITE-DIFFERENCE SCHEMES; MATHEMATICAL-MODEL; NUMERICAL-METHOD; NONSTANDARD; DISCRETIZATION; PRINCIPLE;
D O I：
10.2478/amcs-2014-0046
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
引用
收藏
页码：635 / 646
页数：12
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