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 R0 > 1. Here, we show that the endemic equilibrium is globally stable for R0 > 1. The proof uses a Lyapunov functional that includes an integral over all previous states.
McCluskey, C. Connell, "Global Stability for an SEIR Epidemiological Model with Varying Infectivity and Infinite Delay" (2009). Mathematics Faculty Publications. 11.