Threshold dynamics for SIR epidemic model in periodic environments

The global dynamics of a periodic SIR epidemic model is investigated. The basic reproductive number R
0
is deňed. It is proved that the disease-free equilibrium is globally stable if R
0
<1. The disease-free equilibrium is unstable and the disease remains endemic when R
0
>1, The existence of the periodic solution is investigated and it is proved that the periodic model has at least one periodic solution if R
0
>1 Numerica simulations are also provided to coňrmouranalytic results.