### Mathematical Biosciences and Engineering

2015, Issue 3: 555-564. doi: 10.3934/mbe.2015.12.555

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

• 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

### Related Papers:

• 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.

 [1] J. Math. Biol., 53 (2006), 421-436. [2] 2014, preprint. [3] J. Math. Biol., 62 (2011), 741-762. [4] Math. Biosci., 210 (2007), 647-658. [5] Nonlinear Anal., 74 (2011), 3548-3555. [6] Rocky Mountain J. Math., 9 (1979), 31-42. [7] Proc. R. Soc. B., 273 (2006), 2541-2550. [8] Bull. Math. Biol., 72 (2010), 1192-1207. [9] J. Math. Biol., 65 (2012), 623-652. [10] SIAM J. Appl. Math., 70 (2010), 2023-2044. [11] Nonlinear Anal. RWA, 11 (2010), 3106-3109. [12] Nonlinear Anal. RWA, 11 (2010), 55-59. [13] Appl. Math. Lett., 17 (2004), 1141-1145. [14] SIAM J. Math. Anal., 37 (2005), 251-275. [15] J. Math. Anal. Appl., 363 (2010), 230-237. [16] J. Math. Biol., 64 (2012), 933-949. [17] Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 1155-1170. [18] Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995. [19] J. Integral Equations, 7 (1984), 253-277. [20] J. Math. Biol., 30 (1992), 755-763. [21] SIAM J. Appl. Math., 69 (2008), 621-639. [22] J. Dyn. Diff. Equat., 20 (2008), 699-717. [23] Nonlinear Anal. RWA, 10 (2009), 3175-3189. [24] Math. Biosci., 208 (2007), 419-429. [25] Springer-Verlag, New York, 2003. [26] J. Math. Anal. Appl., 325 (2007), 496-516.
• ##### Reader Comments
• © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

1.285 1.3

## Metrics

Article views(89) PDF downloads(459) Cited by(6)

Article outline

## Other Articles By Authors

• On This Site
• On Google Scholar

/

DownLoad:  Full-Size Img  PowerPoint