Stability criteria for SIS epidemiological models under switching policies

Mustapha Ait Rami; Vahid S. Bokharaie; Oliver Mason; Fabian R. Wirth

doi:10.3934/dcdsb.2014.19.2865

Article Contents

2014, Volume 19, Issue 9: 2865-2887. Doi: 10.3934/dcdsb.2014.19.2865

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Stability criteria for SIS epidemiological models under switching policies

1.
Laboratoire de Modélisation, Information et Systèmes (MIS), University of Picardie Jules Verne, 80025 Amiens
2.
Departement Werktuigkunde, KU Leuven, Leuven
3.
Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare
4.
Dept. of Computer Science and Mathematics, University of Passau, 94030 Passau

Received: June 2013

Revised: April 2014

Published: November 2014

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Abstract

We study the spread of disease in an SIS model for a structured population. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold parameter for this model in the spirit of the basic reproduction number for time-invariant models. We also present conditions for persistence and the existence of periodic orbits for the switched model and results for a stochastic switched model.

Keywords:

Mathematics Subject Classification: Primary: 92D30, 34D23, 37B25.

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