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Threshold dynamics in a time-delayed periodic SIS epidemic model

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  • 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.
    Mathematics Subject Classification: 92D30, 34K13, 37N25.

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