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Mathematical Modeling and Analysis of an Epidemic Model with Quarantine, Latent and Media Coverage
  
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KeyWord:Epidemic model; Stability; Hopf bifurcation; Delay
Author NameAffiliation
Bilal Boulfoul Department of Petrochemical and Process Engineering, Faculty of Technology, University of 20 August 1955-Skikda, B. P. 26, Skikda, 21000, Algeria 
Adlen Kerboua Department of Petrochemical and Process Engineering, Faculty of Technology, University of 20 August 1955-Skikda, B. P. 26, Skikda, 21000, Algeria 
Xueyong Zhou School of Mathematics and Statistics, Xinyang Normal University, Xinyang, Henan 464000, China 
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Abstract:
      Epidemic models are very important in today's analysis of diseases. In this paper, we propose and analyze an epidemic model incorporating quarantine, latent, media coverage and time delay. We analyze the local stability of either the disease-free and endemic equilibrium in terms of the basic reproduction number $\mathcal{R}_{0}$ as a threshold parameter. We prove that if $\mathcal{R}_{0}<1,$ the time delay in media coverage can not affect the stability of the disease-free equilibrium and if $\mathcal{R}_{0}>1$, the model has at least one positive endemic equilibrium, the stability will be affected by the time delay and some conditions for Hopf bifurcation around infected equilibrium to occur are obtained by using the time delay as a bifurcation parameter. We illustrate our results by some numerical simulations such that we show that a proper application of quarantine plays a critical role in the clearance of the disease, and therefore a direct contact between people plays a critical role in the transmission of the disease.