Fig. 3.

Corresponding population numbers of solution $\left(S\right(t),V(t),I(t\left)\right)$ to system (1.3) with transmission rates of $\beta =0.39,0.40,0.41,$ and 0.42, respectively. Other given parameters: $(\Lambda ,\mu ,\alpha ,\delta ,\gamma ,\vartheta )=(0.8,3\times {10}^{-5},0.00457,0.128,0.2,0.4)$ and $({\sigma }_1,{\sigma }_2,{\sigma }_3)=(0.0008,0.0004,0.0008)$.