Mathematical analysis of swine influenza epidemic model with optimal control

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• 作者：Mudassar Imran ; Tufail Malik ; Ali R Ansari…
• 关键词：Influenza ; Reproduction number ; Backward bifurcation ; Uncertainty and sensitivity analysis ; Optimal control ; Statistical inference ; 92B08 ; 49J15 ; 34C23
• 刊名：Japan Journal of Industrial and Applied Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：33
• 期：1
• 页码：269-296
• 全文大小：1,051 KB
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• 作者单位：Mudassar Imran (1)
  Tufail Malik (2)
  Ali R Ansari (1)
  Adnan Khan (3)
  
  1. Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Kuwait City, Kuwait
  2. Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, UAE
  3. Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics
  Computational Mathematics and Numerical Analysis
  
• 出版者：Springer Japan
• ISSN：1868-937X

文摘

A deterministic model is designed and used to analyze the transmission dynamics and the impact of antiviral drugs in controlling the spread of the 2009 swine influenza pandemic. In particular, the model considers the administration of the antiviral both as a preventive as well as a therapeutic agent. Rigorous analysis of the model reveals that its disease-free equilibrium is globally asymptotically stable under a condition involving the threshold quantity-reproduction number \({\mathcal {R}}_c\). The disease persists uniformly if \({\mathcal {R}}_c>1\) and the model has a unique endemic equilibrium under certain condition. The model undergoes backward bifurcation if the antiviral drugs are completely efficient. Uncertainty and sensitivity analysis is presented to identify and study the impact of critical model parameters on the reproduction number. A time dependent optimal treatment strategy is designed using Pontryagin’s maximum principle to minimize the treatment cost and the infected population. Finally the reproduction number is estimated for the influenza outbreak and model provides a reasonable fit to the observed swine (H1N1) pandemic data in Manitoba, Canada, in 2009. Keywords Influenza Reproduction number Backward bifurcation Uncertainty and sensitivity analysis Optimal control Statistical inference