Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators
Establishing the global stability of the endemic equilibrium in host-parasite models has made great progress. This progress is mainly due to the adaptation to epidemic models of the Lyapunov function \(V(x)=x-a\ln (\frac{x}{a})\). In most of the investigations graph-theoretic methods are used. The aim of the paper is to show that, while using the same Lyapunov function, sometimes graph theory can be replaced by positive operator theory. The global stability of the endemic equilibrium is shown for an endemic model with infinite-dimensional population structure using a Volterra-like Lyapunov function and the Krein-Rutman theorem.
scientific article; zbMATH DE number 5869874
scientific article