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**The impact of media coverage on the dynamics of infectious disease.**
*(English)*
Zbl 1155.92343

Summary: we give a compartment model to discuss the influence of media coverage to the spreading and controlling of infectious disease in a given region. The model exhibits two equilibria: a disease-free and a unique endemic equilibrium. Stability analysis of the models shows that the disease-free equilibrium is globally asymptotically stable if the reproduction number \((\mathbb R_0)\), which depends on parameters, is less than unity. But if \(\mathbb R_0>1\), it is shown that a unique endemic equilibrium appears, which is asymptotically stable. In a special case, the endemic equilibrium is globally stable. We discuss the role of media coverage on the spreading based on the theory results.

### MSC:

92D30 | Epidemiology |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

34D23 | Global stability of solutions to ordinary differential equations |

### Keywords:

SIRS model
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\textit{Y. Liu} and \textit{J.-A. Cui}, Int. J. Biomath. 1, No. 1, 65--74 (2008; Zbl 1155.92343)

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### References:

[1] | Cui J., J. Dynam. Differential Equations |

[2] | DOI: 10.1258/0956462971919066 |

[3] | DOI: 10.1186/1742-6405-4-10 |

[4] | DOI: 10.3201/eid1002.030732 |

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[6] | DOI: 10.1016/j.jtbi.2003.11.014 |

[7] | DOI: 10.3934/mbe.2004.1.1 · Zbl 1060.92054 |

[8] | DOI: 10.1016/j.mcm.2005.01.007 · Zbl 1066.92046 |

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