Table 3.3.

The local stability of interior equilibrium for the system (2.9)–(2.10)

Interior Equilibrium	Condition for existence	Condition for stability
Ei1	$\text{max}\{\frac{1-\rho }{d},R_0^h,\frac{1-\rho }{\beta +\rho -1}\}>1/\theta$ and (a) $R_0^{\upsilon }<\frac{4}{{(1-\theta )}^2}$ or (b) $R_0^{\upsilon }>\frac{4}{{(1-\theta )}^2}$ & N1 < θ2	Always a saddle
Ei2	Case (1):$\text{max}\{\frac{1-\rho }{d},R_0^h,\frac{1-\rho }{\beta +\rho -1}\}>1/\theta$ and (a) $R_0^{\upsilon }<\frac{4}{{(1-\theta )}^2}$ or (b) $R_0^{\upsilon }>\frac{4}{{(1-\theta )}^2}$ & N2 < θ2 or (c) $R_0^{\upsilon }>\frac{4}{{(1-\theta )}^2}$, N2 > K2; Case (2): $1<R_0^h<1/\theta$ and (a) $R_0^{\upsilon }<\frac{4}{{(1-\theta )}^2}$ or (b) $R_0^{\upsilon }>\frac{4}{{(1-\theta )}^2}$, N2 < θ2 or (c) $R_0^{\upsilon }>\frac{4}{{(1-\theta )}^2}$, N2 > K2	Locally asymptotically stable if $N_2^{*}>\frac{1+\theta }{2}$ while it’s a source if $\frac{1+\theta }{2}-\frac{\beta }{2(1-\rho )}<N_2^{*}<\frac{1+\theta }{2}$