# American Institute of Mathematical Sciences

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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