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On the Stability of a SEIR Reaction Diffusion Model for Infections Under Neumann Boundary Conditions

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Abstract

This paper deals with a reaction-diffusion SEIR model for infections under homogeneous Neumann boundary conditions. The longtime behaviour of the solutions is analyzed and, in particular, absorbing sets in the phase space are determined. By using a peculiar Lyapunov function, the nonlinear asymptotic stability of endemic equilibrium is investigated.

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Acknowledgements

This paper has been performed under the auspices of the G.N.F.M. of I.N.d.A.M. and Progetto Giovani G.N.F.M. 2013 “Moti fluidi di miscele in strati porosi, immersi in campi termici non isotermi”. The authors thank gratefully Prof. Rionero for having proposed the research and for his helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Applications ‘R. Caccioppoli’, University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cinzia, 80126, Naples, Italy

    F. Capone, V. De Cataldis & R. De Luca

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  1. F. Capone
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  2. V. De Cataldis
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  3. R. De Luca
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Correspondence to V. De Cataldis.

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In honor of Professor Salvatore Rionero, in the occasion of his 80th birthday.

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Capone, F., De Cataldis, V. & De Luca, R. On the Stability of a SEIR Reaction Diffusion Model for Infections Under Neumann Boundary Conditions. Acta Appl Math 132, 165–176 (2014). https://doi.org/10.1007/s10440-014-9899-7

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  • DOI: https://doi.org/10.1007/s10440-014-9899-7

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