Stability Criteria for SIS Epidemiological Models under Switching Policies

2013/06/01 by Mustapha Ait Rami, Vahid Bokharaie, Rami, Mustapha Ait +7
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #34D23 #37B25 #92D30 #COVID-19 epidemiological studies #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #math.DS #math.OC #msc:34D23 #msc:37B25 #msc:92D30

paper · pdf · doi:10.48550/arxiv.1306.0135

openalex publication_date 2013/06/01 · arxiv created 2014/04/17 · arxiv updated 2014/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spread of disease in an SIS model. 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.

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