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.
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Research supported by the NNSF of China (10471066).
Research supported by NSERC, MITACS and CFI/OIT of Canada.
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Cui, J., Sun, Y. & Zhu, H. The Impact of Media on the Control of Infectious Diseases. J Dyn Diff Equat 20, 31–53 (2008). https://doi.org/10.1007/s10884-007-9075-0
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DOI: https://doi.org/10.1007/s10884-007-9075-0