Uniform boundedness of the attractor in \(H^2\) of a non-autonomous epidemiological system

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Abstract

In this paper, we prove the uniform boundedness of the pullback attractor of a non-autonomous SIR (susceptible, infected, recovered) model from epidemiology considered in Anguiano and Kloeden (Commun Pure Appl Anal 13(1):157–173, 2014). We prove two uniform bounds of this pullback attractor, firstly in the norm \(H_0^1\) and later, under appropriate additional assumptions, in the norm \(H^2\).

Keywords

SIR epidemic model with diffusion Invariant sets Uniform boundedness in \(H^2\) 

Mathematics Subject Classification

35B41 37B55 

Notes

Acknowledgements

María Anguiano has been supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de SevillaSevilleSpain

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