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Computational and Mathematical Methods in Medicine
Volume 2018, Article ID 7321694, 11 pages
https://doi.org/10.1155/2018/7321694
Research Article

Global Dynamics of an Avian Influenza A(H7N9) Epidemic Model with Latent Period and Nonlinear Recovery Rate

School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Correspondence should be addressed to Youping Yang; nc.ude.unds@gnayy

Received 18 October 2017; Accepted 22 January 2018; Published 22 February 2018

Academic Editor: Konstantin Blyuss

Copyright © 2018 Rui Mu and Youping Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Liu, H. Xiao, Y. Wu et al., “H7N9: A low pathogenic avian influenza A virus infecting humans,” Current Opinion in Virology, vol. 5, no. 1, pp. 91–97, 2014. View at Publisher · View at Google Scholar · View at Scopus
  2. R. E. Kahn and J. A. Richt, “The novel H7N9 influenza a virus: Its present impact and indeterminate future,” Vector-Borne and Zoonotic Diseases, vol. 13, no. 6, pp. 347-348, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. Study Fingers Chickens, Quail, In Spread Of H7N9 Influenza Virus, 2014, https://www.sciencedaily.com/releases/2014/03/140318093722.htm.
  4. S. Iwami, Y. Takeuchi, and X. Liu, “Avian-human influenza epidemic model,” Mathematical Biosciences, vol. 207, no. 1, pp. 1–25, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Z. Liu and C.-T. Fang, “A modeling study of human infections with avian influenza A H7N9 virus in mainland China,” International Journal of Infectious Diseases, vol. 41, pp. 73–78, 2015. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Liu, S. Ruan, and X. Zhang, “Nonlinear dynamics of avian influenza epidemic models,” Mathematical Biosciences, vol. 283, pp. 118–135, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. Funk, E. Gilad, C. Watkins, and V. A. A. Jansen, “The spread of awareness and its impact on epidemic outbreaks,” Proceedings of the National Acadamy of Sciences of the United States of America, vol. 106, no. 16, pp. 6872–6877, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Wang, B. J. Cowling, P. Wu et al., “Human exposure to live poultry and psychological and behavioral responses to influenza A(H7N9), China,” Emerging Infectious Diseases, vol. 20, no. 8, pp. 1296–1305, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. P. Wu, L. Wang, B. J. Cowling et al., “Live poultry exposure and public response to influenza A(H7N9) in urban and rural China during two epidemic waves in 2013-2014,” PLoS ONE, vol. 10, no. 9, Article ID e0137831, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Ruan and W. Wang, “Dynamical behavior of an epidemic model with a nonlinear incidence rate,” Journal of Differential Equations, vol. 188, no. 1, pp. 135–163, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Liu, L. Pang, S. Ruan, and X. Zhang, “Global dynamics of avian influenza epidemic models with psychological effect,” Computational and Mathematical Methods in Medicine, vol. 2015, Article ID 913726, 2015. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Liu, J. Wu, and H. Zhu, “Media/psychological impact on multiple outbreaks of emerging infectious diseases,” Computational and Mathematical Methods in Medicine, vol. 8, no. 3, pp. 153–164, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Xiao, T. Zhao, and S. Tang, “Dynamics of an infectious diseases with media/psychology induced non-smooth incidence,” Mathematical Biosciences and Engineering, vol. 10, no. 2, pp. 445–461, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. W. Qin, S. Tang, C. Xiang, and Y. Yang, “Effects of limited medical resource on a Filippov infectious disease model induced by selection pressure,” Applied Mathematics and Computation, vol. 283, pp. 339–354, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. WHO, Dengue and dengue naemorrhagic fever, Fact Sheet 117, 2012.
  16. A. Abdelrazec, J. Bélair, C. Shan, and H. Zhu, “Modeling the spread and control of dengue with limited public health resources,” Mathematical Biosciences, vol. 271, pp. 136–145, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  17. W. M. Liu, S. A. Levin, and Y. Iwasa, “Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models,” Journal of Mathematical Biology, vol. 23, no. 2, pp. 187–204, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  18. C. Shan and H. Zhu, “Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds,” Journal of Differential Equations, vol. 257, no. 5, pp. 1662–1688, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts, “The construction of next-generation matrices for compartmental epidemic models,” Journal of the Royal Society Interface, vol. 7, no. 47, pp. 873–885, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J. Lucchetti, M. Roy, and M. Martcheva, “An avian influenza model and its fit to human avian influenza cases,” Advances in Disease Epidemiology, pp. 1–30, 2009. View at Google Scholar · View at Scopus
  22. S. M. Blower and H. Dowlatabadi, “Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example,” International Statistical Review, vol. 62, no. 2, pp. 229–243, 1994. View at Publisher · View at Google Scholar
  23. S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology, vol. 254, no. 1, pp. 178–196, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. S. Liu, S. Ruan, and X. Zhang, “On avian influenza epidemic models with time delay,” Theory in Biosciences, vol. 134, no. 3-4, pp. 75–82, 2015. View at Publisher · View at Google Scholar · View at Scopus
  25. L. Zhou, R. Ren, L. Yang et al., “Sudden increase in human infection with avian influenza A(H7N9) virus in China, September-December 2016,” Western Pacific surveillance and response journal : WPSAR, vol. 8, no. 1, pp. 6–14, 2017. View at Publisher · View at Google Scholar · View at Scopus
  26. X.-Y. Zhao, S.-M. Guo, M. Ghosh, and X.-Z. Li, “Stability and persistence of an avian influenza epidemic model with impacts of climate change,” Discrete Dynamics in Nature and Society, vol. 2016, Article ID 7871251, 2016. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Xiao, X. Sun, S. Tang, and J. Wu, “Transmission potential of the novel avian influenza A(H7N9) infection in mainland China,” Journal of Theoretical Biology, vol. 352, pp. 1–5, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus