Threshold dynamics for SIR epidemic model in periodic environments

The global dynamics of a periodic SIR epidemic model is investigated. The basic reproductive number Ro is dehed. It is proved that the disease-free equilibrium is globally stable if R₀<;1. The disease-free equilibrium is unstable and the disease remains endemic when R₀ > 1, The existence of the periodic solution is investigated and it is proved that the periodic model has at least one periodic solution if R₀>. Numerica simulations are also provided to con´rm ouranalytic results.