Persistence in some periodic epidemic models with infection age or constant periods of infection

Carlota Rebelo; Alessandro Margheri; Nicolas Bacaër

doi:10.3934/dcdsb.2014.19.1155

Article Contents

2014, Volume 19, Issue 4: 1155-1170. Doi: 10.3934/dcdsb.2014.19.1155

This issue Previous Article Multistability and localized attractors in a dissipative discrete NLS equation Next Article Asymptotic pattern of a migratory and nonmonotone population model

Persistence in some periodic epidemic models with infection age or constant periods of infection

1.
Centro de Matemática e Aplicações Fundamentais, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa
2.
IRD and University Paris 6, Research group UMMISCO, Bondy

Received: June 2013

Revised: February 2014

Published: June 2014

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Abstract

Much recent work has focused on persistence for epidemic models with periodic coefficients. But the case where the infected compartments satisfy a delay differential equation or a partial differential equation does not seem to have been considered so far. The purpose of this paper is to provide a framework for proving persistence in such a case. Some examples are presented, such as a periodic SIR model structured by time since infection and a periodic SIS delay model.

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Mathematics Subject Classification: Primary: 92D30, 45J05; Secondary: 54H20.

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