Periodic orbits of a seasonal SIS epidemic model with migration

SARI, Nadir; AUGERAUD VERON, Emmanuelle

doi:10.1016/j.jmaa.2014.10.084

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SARI, Nadir

AUGERAUD VERON, Emmanuelle

Groupe de Recherche en Economie Théorique et Appliquée [GREThA]

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Journal of Mathematical Analysis and Applications. 2015-03-01, vol. 423, n° 2, p. 1849-1866

Resumen en inglés

We consider a seasonally forced SIS epidemic model where the population is spatially divided into two patches. We consider that periodicity occurs in the contact rates by switching between two levels. The epidemic dynamics are described by a switched system. We prove the existence of an invariant domain D containing at least one periodic solution. By considering small migrations, we rewrite the SIS model as a slow-fast dynamical system and show that it has a harmonic periodic solution which lies in a small tubular neighborhood of a curve . We deduce from this study the persistence or not of the disease in each patch.< Leer menos

Palabras clave en inglés

Periodic SIS epidemic model

Migrations

Slow-fast system

Averaging

Periodic motion

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