Fig. 4.

Corresponding simulation of solution $\left(S\right(t),V(t),I(t\left)\right)$ to system (1.3) with vaccination rate $\vartheta =0.371,0.386,0.401,$ and 0.416, respectively. Other fixed parameters: $(\Lambda ,\beta ,\mu ,\alpha ,\delta ,\gamma )=(0.8,0.4,3\times {10}^{-5},0.00457,0.128,0.2)$ and $({\sigma }_1,{\sigma }_2,{\sigma }_3)=(0.0008,0.0004,0.0008)$.