Mathematical Biosciences and Engineering (May 2009)

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

  • C. Connell McCluskey

DOI
https://doi.org/10.3934/mbe.2009.6.603
Journal volume & issue
Vol. 6, no. 3
pp. 603 – 610

Abstract

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A recent paper (Math. Biosci. and Eng. (2008) 5:389-402)presented an SEIR model using an infinite delay to account for varyinginfectivity. The analysis in that paper did not resolve the globaldynamics for R0 >1. Here, we show that the endemic equilibriumis globally stable for R0 >1. The proof uses a Lyapunovfunctional that includes an integral over all previous states.

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