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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 3: 555-564. doi: 10.3934/mbe.2015.12.555
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Threshold dynamics of a periodic SIR model with delay in an infected compartment

  • 1.
    School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071
  • Received: 01 March 2014 Accepted: 29 June 2018 Published: 01 January 2015

  • MSC : Primary: 34K13, 92D30; Secondary: 37N25.

  • Threshold dynamics of epidemic models in periodic environmentsattract more attention. But there are few papers which are concernedwith the case where the infected compartments satisfy a delaydifferential equation. For this reason, we investigate the dynamicalbehavior of a periodic SIR model with delay in an infectedcompartment. We first introduce the basic reproduction number$\mathcal {R}_0$ for the model, and then show that it can act as athreshold parameter that determines the uniform persistence orextinction of the disease. Numerical simulations are performed toconfirm the analytical results and illustrate the dependence of$\mathcal {R}_0$ on the seasonality and the latent period.

    Citation: Zhenguo Bai. Threshold dynamics of a periodic SIR model with delay in an infected compartment[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 555-564. doi: 10.3934/mbe.2015.12.555

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  • Threshold dynamics of epidemic models in periodic environmentsattract more attention. But there are few papers which are concernedwith the case where the infected compartments satisfy a delaydifferential equation. For this reason, we investigate the dynamicalbehavior of a periodic SIR model with delay in an infectedcompartment. We first introduce the basic reproduction number$\mathcal {R}_0$ for the model, and then show that it can act as athreshold parameter that determines the uniform persistence orextinction of the disease. Numerical simulations are performed toconfirm the analytical results and illustrate the dependence of$\mathcal {R}_0$ on the seasonality and the latent period.


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