 Using Lyapunov function theory and LaSalle Invariance Principle, the DFE is shown globally asymptotically stable under some parametric conditions .
<meaning-changed>  Using Lyapunov function theory and LaSalle Invariance Principle, the DFE is shown globally asymptotically stable under some parametric conditions .
 Using Lyapunov function theory and LaSalle Invariance Principle, the disease-free equilibrium is shown globally asymptotically stable under some parametric conditions .