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2009, 6(3): 603-610. doi: 10.3934/mbe.2009.6.603

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

 1 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

Received  September 2008 Revised  December 2008 Published  June 2009

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.
Citation: C. Connell McCluskey. Global stability for an SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences & Engineering, 2009, 6 (3) : 603-610. doi: 10.3934/mbe.2009.6.603
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