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Zbl 1160.34045
Cui, Jingan; Sun, Yonghong; Zhu, Huaiping
The impact of media on the control of infectious diseases. (English)
[J] J. Dyn. Differ. Equations 20, No. 1, 31-53 (2008). ISSN 1040-7294; ISSN 1572-9222/e

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.
[Meng Fan (Changchun)]

MSC 2000:: *34C60 Applications of qualitative theory of ODE
92D30 Epidemiology
34C23 Bifurcation (periodic solutions)
34C05 Qualitative theory of some special solutions of ODE

Keywords: infectious disease; SIE model; media impact; Hopf bifurcation; multiple outbreaks

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