# American Institute of Mathematical Sciences

2015, 12(3): 555-564. doi: 10.3934/mbe.2015.12.555

## 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, China

Received  March 2014 Revised  December 2014 Published  January 2015

Threshold dynamics of epidemic models in periodic environments attract more attention. But there are few papers which are concerned with the case where the infected compartments satisfy a delay differential equation. For this reason, we investigate the dynamical behavior of a periodic SIR model with delay in an infected compartment. We first introduce the basic reproduction number $\mathcal {R}_0$ for the model, and then show that it can act as a threshold parameter that determines the uniform persistence or extinction of the disease. Numerical simulations are performed to confirm 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. Mathematical Biosciences & Engineering, 2015, 12 (3) : 555-564. doi: 10.3934/mbe.2015.12.555
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##### References:
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