Table 1.

All results proved for the system of Equations 1–5.

	Condition	Result
i.	κ1 > 1 and R0 < 1	Disease-free equilibrium is LAS
ii.	κ1 ≤ 1 ⇒ R1 < 1 and R0 ≥ 1 with r = ϵ = 1	Susceptible extinction equilibrium is LAS
iii.	${\kappa }_1>\frac{(\eta +{\mu }_1)(v_1+v_2+{\mu }_2)}{\eta {\mu }_2}$ and T1 + T2 + T3 + T4 + T5 < 1	Disease-free equilibrium is GS
iv.	r = ϵ = 1, κ1 ≤ 1 ⇒ R1 < 1 and ${\kappa }_2>\frac{\eta +{\mu }_1+\alpha }{\eta }$	Susceptible extinction equilibrium is GS
v.	r = ϵ = 1, κ1 ≤ 1⇒R1 < 1 and R0 < 1	Trivial equilibrium is GS

Here, LAS means locally asymptotically stable, and GS means globally stable.