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

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

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.
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Keywords Lyapunov functional.; infinite delay; global stability

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

 

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