zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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 $\Bbb R_0$ 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:
92D30Epidemiology
34D23Global stability of ODE
WorldCat.org
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.%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. · Zbl 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