# American Institute of Mathematical Sciences

October  2017, 14(5&6): 1317-1335. doi: 10.3934/mbe.2017068

## An SEI infection model incorporating media impact

 1 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China 2 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China 3 Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA

1 Author to whom correspondence should be addressed

Received  July 08, 2016 Revised  November 07, 2016 Published  May 2017

To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number $\Re_0$ for the model, and show that the modeled disease dies out regardless of initial infections when $\Re_0 < 1$, and becomes uniformly persistently endemic if $\Re_0>1$. When the disease is endemic and the influence of the media coverage is less than or equal to a critical number, there exists a unique endemic equilibrium which is asymptotical stable provided $\Re_0$ is greater than and near one. However, if $\Re_0$ is larger than a critical number, the model can undergo Hopf bifurcation such that multiple endemic equilibria are bifurcated from the unique endemic equilibrium as the influence of the media coverage is increased to a threshold value. Using numerical simulations we obtain results on the effects of media coverage on the endemic that the media coverage may decrease the peak value of the infectives or the average number of the infectives in different cases. We show, however, that given larger $\Re_0$, the influence of the media coverage may as well result in increasing the average number of the infectives, which brings challenges to the control and prevention of infectious diseases.

Citation: Xuejuan Lu, Shaokai Wang, Shengqiang Liu, Jia Li. An SEI infection model incorporating media impact. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1317-1335. doi: 10.3934/mbe.2017068
##### References:

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##### References:
Effects of media impact $a$ on the value of $S(t), I(t)$ under different media impacts. Here, $\gamma=0.05$ and the initial point are all ($5\times 10^{6}$, 1, 1); $\Re_0=1.1765$ and $R_{H_0}=5.5206$
Effects of media impact $a$ on the value of $S(t), I(t)$ under different media impacts. Here $\gamma=0.02$, the initial point is ($5\times 10^{6}$, 1, 1); $\Re_0=3$ and $R_{H_0}=8.2523$
The peak value of the infective number $I_{max}$ when $a$ from 0 to $a=1 \times 10^{-8}$
Endemic equilibrium $(S^*, E^*, I^*)$ when $a>0$ is varied. In the table, expect for the parameters given in Table 2, here we have $\gamma=0.05.$ In this case, $\Re_0=1.1765$ and $R_{H_{0}}=5.5206$
 Parameter a $S^*$ $E^*$ $I^*$ $a=0$ 4208333 6597 13194 $a=1 \times 10^{-11}$ 4215551 6548 13096 $a=1 \times 10^{-10}$ 4272153 6157 12314
 Parameter a $S^*$ $E^*$ $I^*$ $a=0$ 4208333 6597 13194 $a=1 \times 10^{-11}$ 4215551 6548 13096 $a=1 \times 10^{-10}$ 4272153 6157 12314
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