Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Stability criteria for SIS epidemiological models under switching policies

Pages: 2865 - 2887, Volume 19, Issue 9, November 2014      doi:10.3934/dcdsb.2014.19.2865

       Abstract        References        Full Text (466.7K)       Related Articles       

Mustapha Ait Rami - Laboratoire de Modélisation, Information et Systèmes (MIS), University of Picardie Jules Verne, 80025 Amiens, France (email)
Vahid S. Bokharaie - Departement Werktuigkunde, KU Leuven, Leuven, Belgium (email)
Oliver Mason - Hamilton Institute, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland (email)
Fabian R. Wirth - Dept. of Computer Science and Mathematics, University of Passau, 94030 Passau, Germany (email)

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:  Mathematical epidemiology, SIS model, compartmental model, switched system, disease propagation, endemic equilibrium, positive system, extremal norm, Lyapunov exponents.
Mathematics Subject Classification:  Primary: 92D30, 34D23, 37B25.

Received: June 2013;      Revised: April 2014;      Available Online: September 2014.