##
**An SIS infection model incorporating media coverage.**
*(English)*
Zbl 1170.92024

Summary: We develop a model to explore the impact of media coverage on the control of spreading of emerging or reemerging infectious diseases in a given population. The model can have up to two equilibria: a disease free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease free equilibrium is globally asymptotically stable if the reproduction number \(\mathbb R_0\) is less than unity, and the endemic equilibrium is globally asymptotically stable when it exists. Though the media coverage itself is not a determined fact to eradicate the infection of the diseases, the analysis of the model indicates that, to a certain extent, the more media coverage in a given population, the less number of individuals will be infected. Therefore, media coverage is critical for educating people in understanding the possibility of being infected by the disease.

PDFBibTeX
XMLCite

\textit{J.-A. Cui} et al., Rocky Mt. J. Math. 38, No. 5, 1323--1334 (2008; Zbl 1170.92024)

Full Text:
DOI

### References:

[1] | F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemics , Springer-Verlag, New York, 2000. · Zbl 1302.92001 |

[2] | J. Cui, Y. Sun and H. Zhu, The impact of media on the spreading and control of infectious disease , J. Dynamics Differential Equations 20 (2008), 31-53. · Zbl 1160.34045 |

[3] | J. Cui, Y. Takeuchi and Y. Saito, Spreading disease with transport-related infection , J. Theoretical Biol. 239 (2006), 376-390. |

[4] | O. Diekmann and J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases : Model building, analysis and interpretation , Wiley, New York, 2000. · Zbl 0997.92505 |

[5] | Health Canada, Website:, http://www.hc-sc.gc.ca/pphb-dgspsp/sars-sras/prof-e.html. |

[6] | W. Kermack and A. McKendrick, Contributions to the mathematical theory of epidemic , Proc. Roy. Soc. London 115 (1927), 700-721. · JFM 53.0517.01 |

[7] | M.A. Khan, M. Rahman, P.A. Khanam, B.E. Khuda, T.T. Kane and A. Ashraf, Awareness of sexually transmitted diseases among woman and service providers in rural Bangladesh , International J. STD AIDS 8 (1997), 688-696. |

[8] | Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease , International J. Biomath. 1 (2008), 1-10. · Zbl 1155.92343 |

[9] | R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases , Comp. Math. Methods Medicine 8 (2007), 153-164. · Zbl 1121.92060 |

[10] | L. Perko, Differential equations and dynamic systems , Springer, New York, 1996. · Zbl 0854.34001 |

[11] | M.S. Rahman and M.L. Rahman, Media and education play a tremendous role in mounting AIDS awareness among married couples in Bangladesh, AIDS Research Therapy 4 (2007), 10-17. |

[12] | SARS EXPRESS: http://www.syhao.com/sars, /20030623.htm. |

[13] | Z. Shen, et al., Superspreading SARS events, Beijing, 2003. Emerging Infectious Diseases 10 (2004), 256-260. |

[14] | P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission , Math. Biosci. 180 (2002), 29-48. · Zbl 1015.92036 |

[15] | W. Wang and S. Ruan, Simulating the SARS outbreak in Beijing with limited data, J. Theoret. Biol. 227 (2004), 369-379. |

[16] | Webb, Blaser, Zhu, Aradl and Wu, Critical role of nosocomial transmission in the Toronto SARS outbreak, Math. Biosci. Engineering 1 (2004), 1-13. · Zbl 1060.92054 |

[17] | WHO, Epidemic curves : Serve acute respiratory syndrome (SARS), http://www.who.int/csr/sars/epicurve/epiindex/en/print.html. |

[18] | Y. Zhou, Z. Ma and F. Brauer, A discrete epidemic model for SARS transmission and control in China, Math. Computer Model. 40 (2004), 1491-1506. · Zbl 1066.92046 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.