A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence

Abstract

Explicit Lyapunov functions for SIR and SEIR compartmentalepidemic models with nonlinear incidence of the form $\beta I^p S^q$for the case $p \leq 1$are constructed. Global stability of the models is thereby established.

Keywords

• nonlinear incidence.
• endemic equilibrium state
• global stability
• direct lyapunov method