Figure 1

Stability of disease-free equilibrium. The parameters are fixed as follows: ${\beta }_1=0.0025$, ${\beta }_p=0.0025$, ${\beta }_s=0.0001$, ${\alpha }_1=0.1$, ${\alpha }_p=0.2$, ${\alpha }_s=0.2$, $\mu =0.1$, $\gamma =0.4$, $K=1\text{,}000$, $\mathrm{\Lambda }=5$, $m=0.3$, $d=0.1$, and the initial values are $(S_0,I_0,Y_0)=(700,200,10)$. The time series charts for $S(t)$, $I(t)$, $Y(t)$ and the phase diagram are given in (A), (B), (C), and (D), respectively.