Positive Periodic Solutions of an Epidemic Model with Seasonality

Figure 1

𝑅_𝑑 in terms of 𝑅₀. The region of 𝑂₁, 𝑂₂, and 𝑂₃ is the basin of attraction of equilibrium 𝑂; the region of 𝐸₀ is the basin of attraction of equilibrium 𝐸₀; the region of 𝐸_∗ is the basin of attraction of equilibrium 𝐸_∗; the line 𝐿 is 𝑅_𝑑=𝑅₁=1+𝜇(𝑚+𝜇)(𝑚+𝜎)(𝑅₀−1)/𝑚𝛽(𝑚+𝜎+𝜇).