Threshold dynamics of a periodic SIR model with delay in an infected compartment

Zhenguo Bai

doi:10.3934/mbe.2015.12.555

Article Contents

2015, Volume 12, Issue 3: 555-564. Doi: 10.3934/mbe.2015.12.555

This issue Previous Article Cell scale modeling of electropermeabilization by periodic pulses Next Article Network-level reproduction number and extinction threshold for vector-borne diseases

Threshold dynamics of a periodic SIR model with delay in an infected compartment

Zhenguo Bai^1,

1.
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071

Received: March 2014

Revised: December 2014

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 34K13, 92D30; Secondary: 37N25.

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