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

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• 作者：Qianqian Cui (4) (5)
  Jiabo Xu (6)
  Qiang Zhang (5)
  Kai Wang (7)
  
  4. Department of Applied Mathematics ; Nanjing University of Science and Technology ; Nanjing ; 210094 ; People鈥檚 Republic of China
  5. College of Sciences ; Shihezi University ; Shihezi ; 832000 ; People鈥檚 Republic of China
  6. Xinjiang Institute of Engineering ; Urumqi ; 830091 ; People鈥檚 Republic of China
  7. Department of Medical Engineering and Technology ; Xinjiang Medical University ; Urumqi ; 830011 ; People鈥檚 Republic of China
  
• 关键词：mathematical model ; transmission dynamics ; basic reproduction number ; sensitivity analysis ; control strategies
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：393 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

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.