Table 3.2.

The local stability of interior equilibrium for the system (2.7)–(2.8)

Interior Equilibrium	Condition for existence	Condition for local asymptotically stable
Ei1	$R_0^{\upsilon }<\frac{4}{{(1-\theta )}^2}<\frac{1-\rho }{\beta -d}$ or $\frac{4}{{(1-\theta )}^2}<R_0^{\upsilon }<\frac{1-\rho }{\beta -d}$	Always a saddle
Ei2	$R_0^{\upsilon }<\frac{4}{{(1-\theta )}^2}<\frac{1-\rho }{\beta -d}$ or $\frac{4}{{(1-\theta )}^2}<R_0^{\upsilon }<\frac{1-\rho }{\beta -d}$	Always locally asymptotically stable.