Impact of heterogeneity on the dynamics of an SEIR epidemic model

Zhisheng Shuai; P. van den Driessche

doi:10.3934/mbe.2012.9.393

Article Contents

2012, Volume 9, Issue 2: 393-411. Doi: 10.3934/mbe.2012.9.393

This issue Previous Article Optimal control of chikungunya disease: Larvae reduction, treatment and prevention Next Article The impact of school closures on pandemic influenza: Assessing potential repercussions using a seasonal SIR model

Impact of heterogeneity on the dynamics of an SEIR epidemic model

Zhisheng Shuai^1, and
P. van den Driessche^1,

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., V8W 3R4

Received: April 2011

Revised: August 2011

Published: February 2012

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Abstract

An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number $\mathcal{R}_0$ gives a sharp threshold. If $\mathcal{R}_0\leq 1$, then the disease-free equilibrium is globally asymptotically stable and the disease dies out from all groups or stages. If $\mathcal{R}_0>1$, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 34K20.

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