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The impact of media on the control of infectious diseases. (English) Zbl 1160.34045
This paper uses a compartmental model to address the impact of media coverage on the transmission of infectious diseases. The mathematical model is a variant of the standard SIE model governed by ODEs in which the usual $$SI$$ term is multiplied by a factor $$\mu e^{-mI}$$ which decreases exponentially in $$I$$ and the parameter $$m$$ reflects the impact of media coverage to the contact transmission. The studies reveals that the model has a disease free equilibrium which is globally asymptotically stable if the basic reproduction number $$R_0$$ is less than the unity. Conversely, if $$R_0>1$$, then a unique endemic equilibrium appears and a Hopf bifurcation can occur which leads to oscillatory phenomena. Numerical studies show that, if $$R_0>1$$ and the effect of the media coverage is sufficiently strong, the model exhibits multiple positive equilibria which gives rise to challenge to the prediction and control of the outbreaks of infectious diseases.

##### MSC:
 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D30 Epidemiology 34C23 Bifurcation theory for ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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