An NSFD scheme for SIR epidemic models of childhood diseases with constant vaccination strategy

Advances in Difference Equations

Qiang Zhang¹  Qianqian Cui²  Jiabo Xu⁴  Kai Wang⁴ 

[1] College of Sciences, Shihezi University, Shihezi, People’Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, People’Xinjiang Institute of Engineering, Urumqi, People’s Republic of China

关键词: mathematical model;    transmission dynamics;    basic reproduction number;    sensitivity analysis;    control strategies;   

DOI  :  10.1186/1687-1847-2014-172

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we construct a nonstandard finite difference (NSFD) scheme for an SIR epidemic model of childhood disease with constant strategy. The dynamics of the obtained discrete model is investigated. First we show that the discrete model has equilibria which are exactly the same as those of the continuous model. Furthermore, we prove that the conditions for those equilibria to be globally asymptotically stable are consistent with the continuous model for any size of numerical time-step. The analytical results are confirmed by some numerical simulations.

【 授权许可】

CC BY