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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.

##### MSC:
 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations
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##### 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.%DOI:10.1007/s10884-007-9075-0. · Zbl 1160.34045 · doi:10.1007/s10884-007-9075-0 [3] J. Cui, Y. Takeuchi and Y. Saito, Spreading disease with transport-related infection , J. Theoretical Biol. 239 (2006), 376-390. · doi:10.1016/j.jtbi.2005.08.005 [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 · doi:10.1142/S1793524508000023 [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 · doi:10.1080/17486700701425870 · eudml:231020 [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 · doi:10.1016/S0025-5564(02)00108-6 [15] W. Wang and S. Ruan, Simulating the SARS outbreak in Beijing with limited data, J. Theoret. Biol. 227 (2004), 369-379. · doi:10.1016/j.jtbi.2003.11.014 [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 · doi:10.3934/mbe.2004.1.1 [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 · doi:10.1016/j.mcm.2005.01.007
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