Global stability for an SEIR epidemiological model with varying infectivity and infinite delay

Abstract

A recent paper (Math. Biosci. and Eng. (2008) 5:389-402) presented an SEIR model using an infinite delay to account for varying infectivity. The analysis in that paper did not resolve the global dynamics for R<SUB>0</SUB> >1. Here, we show that the endemic equilibrium is globally stable for R<SUB>0</SUB> >1. The proof uses a Lyapunov functional that includes an integral over all previous states.