The Switched SIR Model

  • Xinzhi Liu
  • Peter Stechlinski
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 19)


The modeling of epidemics by hybrid and switched systems is introduced and analyzed. To begin, the classical SIR model is derived and its defining features are detailed. Motivated by variations in the contact rate between members of the population, a switched SIR model is formulated. The flexibility of the switched systems framework and its accompanying theory is highlighted by relaxing some of the population demographics and epidemiological assumptions. A switching incidence rate function form is considered to model abrupt changes in population behavior. The incorporation of stochastic perturbations into the model is also investigated. The findings here focus on the qualitative behavior of the models (i.e., stability theory). More specifically, global attractivity and partial stability are demonstrated, as well as persistence of the disease.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Xinzhi Liu
    • 1
  • Peter Stechlinski
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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