Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases

This paper demonstrates input-to-state stability (ISS) of the SIR model infectious diseases with respect to disease-free equilibrium and endemic equilibrium. Lyapunov functions are constructed verify that both equilibria individually robust perturbation newborn/immigration rate which determines eventual state populations in epidemics. The construction analysis geometric global space populations. In addition establishment ISS, this shows how explicitly level sets reflect flow trajectories. Essential obstacles keys for elucidated. proposed have strictly negative derivative allow us not only establish but also get rid use LaSalle's invariance principle popular simplifying assumptions.