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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 940841, 8 pages
http://dx.doi.org/10.1155/2014/940841
Research Article

Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received 25 February 2014; Revised 12 June 2014; Accepted 13 June 2014; Published 13 July 2014

Academic Editor: Zhichun Yang

Copyright © 2014 Lixia Zuo and Maoxing Liu. 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. World Health Organization, “Global burden of disease: 2004 update,” 2008, http://www.who.int/healthinfo/global-burden-disease/2004reportupdate/en/.
  2. World Health Organization, “Report on the Global AIDS Epidemic,” 2008, http://www.unaids.org/en/KnowledgeCentre/HIVData/Global Report/2008/2008 Global report.asp.
  3. J. G. Breman, M. S. Alilio, and A. Mills, “Conquering the intolerable burden of malaria: what's new, what's needed: a summary,” American Journal of Tropical Medicine and Hygiene, vol. 71, no. 2, pp. 1–15, 2004. View at Scopus
  4. R. Laxminarayan, A. J. Mills, J. G. Breman et al., “Advancement of global health: key messages from the Disease Control Priorities Project,” Lancet, vol. 367, no. 9517, pp. 1193–1208, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. P. L. M. Vasterman and N. Ruigrok, “Pandemic alarm in the Dutch media: media coverage of the 2009 influenza A (H1N1) pandemic and the role of the expert sources,” European Journal of Communication, vol. 28, no. 4, pp. 436–453, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Gao and S. Ruan, “An SIS patch model with variable transmission coefficients,” Mathematical Biosciences, vol. 232, no. 2, pp. 110–115, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. M. Tchuenche, N. Dube, C. P. Bhunu, R. J. Smith, and C. T. Bauch, “The impact of media coverage on the transmission dynamics of human influenza,” BMC Public Health, vol. 11, no. 1, article S5, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Cui, X. Tao, and H. Zhu, “An {SIS} infection model incorporating media coverage,” The Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1323–1334, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. Y. Li and J. Cui, “The effect of constant and pulse vaccination on {SIS} epidemic models incorporating media coverage,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2353–2365, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. Z. Mukandavire, W. Garira, and J. M. Tchuenche, “Modelling effects of public health educational campaigns on {HIV}/{AIDS} transmission dynamics,” Applied Mathematical Modelling, vol. 33, no. 4, pp. 2084–2095, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Samanta, S. Rana, A. Sharma, A. K. Misra, and J. Chattopadhyay, “Effect of awareness programs by media on the epidemic outbreaks: a mathematical model,” Applied Mathematics and Computation, vol. 219, no. 12, pp. 6965–6977, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. K. Misra, A. Sharma, and J. B. Shukla, “Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 1221–1228, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. H. Joshi, S. Lenhart, and K. Albright, “Modeling the effect of information campaigns on the HIV epidemic in Uganda,” Mathematical Biosciences and Engineering, vol. 5, no. 4, pp. 757–770, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. F. Nyabadza, C. Chiyaka, Z. Mukandavire, and S. D. Hove-Musekwa, “Analysis of an HIV/AIDS model with public-health information campaigns and individual withdrawal,” Journal of Biological Systems, vol. 18, no. 2, pp. 357–375, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J. A. Yorke and W. P. London, “Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects,” American Journal of Epidemiology, vol. 98, no. 6, pp. 469–482, 1973. View at Scopus
  16. I. Z. Kiss, J. Cassell, M. Recker, and P. L. Simon, “The impact of information transmission on epidemic outbreaks,” Mathematical Biosciences, vol. 225, no. 1, pp. 1–10, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. V. Capasso, Mathematical Structure of Epidemic System, vol. 97 of Lecture Notes in Biomathematics, Springer, Berlin, Germany, 1993. View at Publisher · View at Google Scholar
  18. H. W. Hethcote and S. A. Levin, “Periodicity in epidemiological models,” in Applied Mathematical Ecology, vol. 18 of Biomathematics, pp. 193–211, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. Collinson and J. M. Heffernan, “Modelling the effects of media during an influenza epidemic,” Collinson and Heffernan BMC Public Health, vol. 14, article 376, 2014. View at Publisher · View at Google Scholar
  20. J. H. Pang and J. A. Cui, “An SIRS epidemiological model with nonlinear incidence rate incorporating media coverage,” in Proceedings of the 2nd International Conference on Information and Computing Science (ICIC '09), pp. 116–119, Manchester, UK, May 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Liu, G. Röst, and G. Vas, “SIS model on homogeneous networks with threshold type delayed contact reduction,” Computers & Mathematics with Applications, vol. 66, no. 9, pp. 1534–1546, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. M. Elenbaas, H. G. Boomgaarden, A. R. T. Schuck, and C. H. de Vreese, “The impact of media coverage and motivation on performance-relevant information,” Political Communication, vol. 30, no. 1, pp. 1–16, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. W. M. Liu, H. W. Hethcote, and S. A. Levin, “Dynamical behavior of epidemiological models with nonlinear incidence rates,” Journal of Mathematical Biology, vol. 25, no. 4, pp. 359–380, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. 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 · View at Scopus
  25. Y. Liu and J. Cui, “The impact of media coverage on the dynamics of infectious disease,” International Journal of Biomathematics, vol. 1, no. 1, pp. 65–74, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. H. Zhao, Y. Lin, and Y. Dai, “An SIRS epidemic model incorporating media coverage with time delay,” Computational and Mathematical Methods in Medicine, vol. 2014, Article ID 680743, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  27. J. M. Tchuenche and C. T. Bauch, “Dynamics of an infectious disease where media coverage influences transmission,” ISRN Biomathematics, vol. 2012, Article ID 581274, 10 pages, 2012. View at Publisher · View at Google Scholar
  28. J. Cui, Y. Sun, and H. Zhu, “The impact of media on the control of infectious diseases,” Journal of Dynamics and Differential Equations, vol. 20, no. 1, pp. 31–53, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. R. S. Liu, J. H. Wu, and H. P. 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 MathSciNet · View at Scopus
  30. Y. Y. Liu and Y. N. Xiao, “An epidemic model with saturated media/psychological impact,” Applied Mathematics and Mechanics, vol. 34, no. 4, pp. 99–407, 2013.
  31. A. Wang and Y. Xiao, “A Filippov system describing media effects on the spread of infectious diseases,” Nonlinear Analysis: Hybrid Systems, vol. 11, pp. 84–97, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. C. P. Bhunu, S. Mushayabasa, and H. Kojouharov, “Mathematical analysis of an {HIV}/{AIDS} model: impact of educational programs and abstinence in sub-Saharan Africa,” Journal of Mathematical Modelling and Algorithms, vol. 10, no. 1, pp. 31–55, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. Y. Wang, J. D. Cao, Z. Jin, H. F. Zhang, and G. Q. Sun, “Impact of media coverage on epidemic spreading in complex networks,” Physica A: Statistical Mechanics and Its Applications, vol. 392, no. 23, pp. 5824–5835, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  34. X. Yuan, Y. Xue, and M. Liu, “Analysis of an epidemic model with awareness programs by media on complex networks,” Chaos, Solitons & Fractals, vol. 48, no. 1, pp. 1–11, 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. 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 Academy 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 Zentralblatt MATH · View at Scopus
  36. W. Liu, “A SIRS epidemic model incorporating media coverage with random perturbation,” Abstract and Applied Analysis, vol. 2013, Article ID 792308, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  37. L. Wang, H. L. Huang, A. C. Xu, and W. M. Wang, “Stochastic extinction in an SIRS epidemic model incorporating media coverage,” Abstract and Applied Analysis, vol. 2013, Article ID 891765, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  38. H. M. Wei, X. Z. Li, and M. Martcheva, “An epidemic model of a vector-borne disease with direct transmission and time delay,” Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 895–908, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus