Open AccessThreshold dynamics of a periodic SIR model with delay in an infected compartment
Author(s) -
Zhenguo Bai
Publication year - 2015
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015.12.555
Subject(s) - epidemic model , persistence (discontinuity) , dynamics (music) , statistical physics , compartment (ship) , basic reproduction number , mathematics , physics , demography , population , oceanography , geotechnical engineering , sociology , acoustics , engineering , geology
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 R0 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 R0 on the seasonality and the latent period.