Figure 2

Bifurcation diagram for system ( 1 ). In region I, the disease-free equilibrium $P_0$ is globally asymptotically stable; in region II, the boundary equilibrium $P_{1\ast }$ is locally stable; in region III, the boundary equilibrium $P_{2\ast }$ is locally stable; and in region IV, the endemic equilibrium $P_{\ast \ast }$ is globally asymptotically stable. In the regions V and VI, the two boundary equilibria are unstable.