Internal eradicability for an epidemiological model with diffusion

Sebastian Aniţa; Bedreddine Ainseba

doi:10.3934/mbe.2005.2.437

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2005, Volume 2, Issue 3: 437-443. Doi: 10.3934/mbe.2005.2.437

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Internal eradicability for an epidemiological model with diffusion

Sebastian Aniţa^1, and
Bedreddine Ainseba^2,

1.
Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506
2.
Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, case 26, Université Bordeaux 2, 33076 Bordeaux Cedex

Received: January 2005

Revised: August 2005

Published: July 2005

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Abstract

This work is concerned with the analysis of the possibility for eradicating a disease in an infected population. The epidemiological model under study is of SI type with diffusion. We assume the policy strategy acting on the infected individuals over a subset of the whole spatial territory. Using the framework of nonlinear reaction-diffusion equations, and spectral theory of linear differential operators, we give necessary conditions and sufficient conditions of eradicability.

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Mathematics Subject Classification: 92D30.

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