Abstract and Applied Analysis

An SIRS Model for Assessing Impact of Media Coverage

Jing’an Cui and Zhanmin Wu

Full-text: Open access


An SIRS model incorporating a general nonlinear contact function is formulated and analyzed. When the basic reproduction number 0 < 1 , the disease-free equilibrium is locally asymptotically stable. There is a unique endemic equilibrium that is locally asymptotically stable if 0 > 1 . Under some conditions, the endemic equilibrium is globally asymptotically stable. At last, we conduct numerical simulations to illustrate some results which shed light on the media report that may be the very effective method for infectious disease control.

Article information

Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 424610, 6 pages.

First available in Project Euclid: 6 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Cui, Jing’an; Wu, Zhanmin. An SIRS Model for Assessing Impact of Media Coverage. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 424610, 6 pages. doi:10.1155/2014/424610. https://projecteuclid.org/euclid.aaa/1412607563

Export citation


  • S. J. Etuk and E. I. Ekanem, “Impact of mass media campaigns on the knowledge and attitudes of pregnant Nigerian woman towards HIV/AIDS,” Tropical Doctor, vol. 35, no. 2, pp. 101–102, 2005.
  • M. S. Rahman and M. L. Rahman, “Media and education play a tremendous role in mounting AIDS awareness among married couples in Banladesh,” AIDS Research and Therapy, vol. 4, no. 1, pp. 1–7, 2007.
  • C. Sun, W. Yang, J. Arino, and K. Khan, “Effect of media-induced social distancing on disease transmission in a two patch setting,” Mathematical Biosciences, vol. 230, no. 2, pp. 87–95, 2011.
  • S. Funk, E. Gilad, and V. A. A. Jansen, “Endemic disease, awareness, and local behavioural response,” Journal of Theoretical Biology, vol. 264, no. 2, pp. 501–509, 2010.
  • J. A. Cui, Y. H. Sun, and H. P. 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.
  • Y. P. Liu and J.-A. Cui, “The impact of media coverage on the dynamics of infectious disease,” International Journal of Biomathematics, vol. 1, no. 1, pp. 65–74, 2008.
  • N. Ferguson, “Capturing human behaviour,” Nature, vol. 446, no. 7137, article 733, 2007.
  • J.-A. Cui, X. Tao, and H. P. Zhu, “An SIS infection model incorporating media coverage,” The Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1323–1334, 2008.
  • 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.
  • R. A. Smith, “Some applications of Hausdorff dimension inequalities for ordinary differential equations,” Proceedings of the Royal Society of Edinburgh A, vol. 104, no. 3-4, pp. 235–259, 1986.
  • M. Y. Li and J. S. Muldowney, “A geometric approach to global-stability problems,” SIAM Journal on Mathematical Analysis, vol. 27, no. 4, pp. 1070–1083, 1996.
  • M. Fan, M. Y. Li, and K. Wang, “Global stability of an SEIS epidemic model with recruitment and a varying total population size,” Mathematical Biosciences, vol. 170, no. 2, pp. 199–208, 2001.
  • G. Butler and P. Waltman, “Persistence in dynamical systems,” Journal of Differential Equations, vol. 63, no. 2, pp. 255–263, 1986.
  • H. I. Freedman, S. G. Ruan, and M. X. Tang, “Uniform persistence and flows near a closed positively invariant set,” Journal of Dynamics and Differential Equations, vol. 6, no. 4, pp. 583–600, 1994.
  • R. H. Martin Jr., “Logarithmic norms and projections applied to linear differential systems,” Journal of Mathematical Analysis and Applications, vol. 45, pp. 432–454, 1974. \endinput