Figure 11.

(a) Bifurcation diagram of system equations (2.1)–(2.5) represented by ${\displaystyle I_1}$ and ${\displaystyle {\mathcal{R}}_c}$ with respect to ${\displaystyle u_2}$ . The solid lines represent the stable branch of the equilibrium point and the dotted line represents the unstable branch of the equilibrium point. The red and cyan curves represent the endemic equilibrium and the ${\displaystyle {\mathcal{R}}_c}$ , respectively. Panels (b) and (c) show trajectories solution of ${\displaystyle S,I_1}$ and ${\displaystyle I_2}$ at two different sample points ${\displaystyle P_1(u_2=0.2)}$ and ${\displaystyle P_2(u_2=0.9)}$ . All solutions were obtained numerically using various initial conditions.