Persistence, Periodicity and Privacy for Positive Systems in Epidemiology and Elsewhere

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 471)


We first recall and describe some recently published results giving sufficient conditions for persistence and the existence of periodic solutions for switched SIS epidemiological models. We extend the result on the existence of persistent switching signals in two ways. We establish uniform strong persistence where previous work only guaranteed weak persistence; we replace the hypothesis that there exists an unstable matrix in the convex hull of the linearized systems with the weaker assumption that the JLE is positive. In the final section of the chapter, the issue of data privacy for positive systems is addressed.


Switched systems SIS models Persistence Joint Lyapunov exponent Differential privacy 



This work was supported, in part, by Science Foundation Ireland grant 13/RC/2094 and co-funded under the European Regional Development Fund through the Southern & Eastern Regional Operational Programme to Lero—the Irish Software Research Centre (


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics & Statistics/Hamilton InstituteMaynooth University and Lero, The Irish Software Research CentreKildareIreland
  2. 2.Department of Mathematics & StatisticsMaynooth University and Lero, The Irish Software Research CentreKildareIreland
  3. 3.Faculty of Computer Science and MathematicsUniversity of PassauPassauGermany

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