The Impact of Media on the Control of Infectious Diseases

  • Jingan Cui
  • Yonghong Sun
  • Huaiping ZhuEmail author

We develop a three dimensional compartmental model to investigate the impact of media coverage to the spread and control of infectious diseases (such as SARS) in a given region/area. Stability analysis of the model shows that the disease-free equilibrium is globally-asymptotically stable if a certain threshold quantity, the basic reproduction number (\(\mathbb R_0\)), is less than unity. On the other hand, if \(\mathbb R_0 > 1\) , it is shown that a unique endemic equilibrium appears and a Hopf bifurcation can occur which causes oscillatory phenomena. The model may have up to three positive equilibria. Numerical simulations suggest that when \(\mathbb R_0 > 1\) and the media impact is stronger enough, the model exhibits multiple positive equilibria which poses challenge to the prediction and control of the outbreaks of infectious diseases.


Infectious disease SEI model media impact Hopf bifurcation multiple outbreaks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brauer F., Castillo-Chavez C.(2000). Mathematical Models in Population Biology and Epidemics. Springer-Verlag, New YorkGoogle Scholar
  2. 2.
    Busenberg S., Cooke K.(1993). Vertically Transmitted Diseases. Springer-Verlag, New YorkzbMATHGoogle Scholar
  3. 3.
    Capasso V.(1993). Mathematical Structure of Epidemic System, Lecture Note in Biomathematics, Vol. 97. Springer, BerlinGoogle Scholar
  4. 4.
    Capasso V., Serio G. (1978). A generalization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci. 42: 43zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Diekmann O., Heesterbeek J.A.P.(2000). Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, New YorkGoogle Scholar
  6. 6.
    Dumortier F., Roussarie R., Sotomayor J.(1987). Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3. Ergodic Theory Dynamical Systems 7(3): 375–413zbMATHMathSciNetGoogle Scholar
  7. 7.
    Health Canada: Scholar
  8. 8.
    Hethcote H.W.(2000). The mathematics of infectious diseases. SIAM Revi. 42, 599–653zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Levin S.A., Hallam T.G., Gross L.J. (1989). Applied Mathematical Ecology. Springer, New YorkzbMATHGoogle Scholar
  10. 10.
    Liu W.M., Hethcote H.W., Levin S.A.(1987). Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol. 25: 359zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Liu W.M., Levin S.A., Iwasa Y.(1986). Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23: 187zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Liu, R., Wu, J., and Zhu, H. (2005). Media/Psychological Impact on Multiple Outbreaks of Emerging Infectious Diseases, preprintGoogle Scholar
  13. 13.
    Murray J.D. (1998). Mathematical Biology. Springer-Verlag, BerlinGoogle Scholar
  14. 14.
    Ruan S., Wang W.(2003). Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Diff. Equs. 188: 135zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    SARS EXPRESS: Scholar
  16. 16.
    Shen Z. et al. (2004). Superspreading SARS events, Beijing, 2003. Emerg. Infect. Dis. 10(2): 256–260Google Scholar
  17. 17.
    van den Driessche P., Watmough J.(2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180: 29–48zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Wang W., Ruan S.(2004). Simulating SARS outbreak in Beijing with limit data. J. Theor. Biol. 227: 369CrossRefMathSciNetGoogle Scholar
  19. 19.
    WHO. Epidemic curves: Serve Acute Respiratory Syndrome (SARS) Scholar
  20. 20.
    Yorke J.A., London W.P.(1973). Recurrent outbreaks of measles, chickenpox and mumps II. Am. J. Epidemiol. 98: 469Google Scholar
  21. 21.
    Zhu H., Campbell S.A., Wolkowicz G.S.(2002). Bifurcation analysis of a predator-prey system with nonmonotonic function response. SIAM J. Appl. Math. 63(2): 636–682zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceNanjing Normal UniversityNanjingChina
  2. 2.Department of Information and TechnologyJiangsu Institute of Economic & Trade Technology JiangningNanjingChina
  3. 3.Department of Mathematics and StatisticsYork UniversityTorontoCanada

Personalised recommendations