July  2009, 12(1): 169-186. doi: 10.3934/dcdsb.2009.12.169

Threshold dynamics in a time-delayed periodic SIS epidemic model

1. 

Department of Mathematics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

2. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NF A1C 5S7

Received  August 2008 Revised  December 2008 Published  May 2009

The global dynamics of a periodic SIS epidemic model with maturation delay is investigated. We first obtain sufficient conditions for the single population growth equation to admit a globally attractive positive periodic solution. Then we introduce the basic reproduction ratio $\mathcal{R}_0$ for the epidemic model, and show that the disease dies out when $\mathcal{R}_0<1$, and the disease remains endemic when $\mathcal{R}_0>1$. Numerical simulations are also provided to confirm our analytic results.
Citation: Yijun Lou, Xiao-Qiang Zhao. Threshold dynamics in a time-delayed periodic SIS epidemic model. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 169-186. doi: 10.3934/dcdsb.2009.12.169
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