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

2009, Volume 6, Issue 3: 603-610. doi: 10.3934/mbe.2009.6.603

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Received: 01 September 2008 Accepted: 29 June 2018 Published: 01 June 2009
MSC : 34K20, 92D30.

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

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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 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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