SIR-Type Epidemic Models as Block-Structured Markov Processes

  • Claude LefèvreEmail author
  • Matthieu Simon


This paper proposes a block-structured Markov process to describe the spread of epidemics of Susceptible-Infected-Removed (SIR) type. Our purpose is to determine the distribution of the final state of the process and of some other interesting measures of the dimension of the epidemic. The followed modeling approach proves to be simple and systematic. Its flexibility is underlined by the presentation of several specific models that extend the classical general epidemic. Finally, two numerical examples illustrate some of the results obtained.


SIR epidemic models Block-structured Markov processes Matrix-analytic methods 

Mathematics Subject Classification (2010)

60J28 60K10 60K37 


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We thank the referees for useful comments and suggestions. M. Simon acknowledges the support of the Australian Research Council Center of Excellence for Mathematical and Statistical Frontiers (ACEMS).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département de Mathématique, Campus Plaine C.P. 210Université Libre de BruxellesBruxellesBelgium
  2. 2.School of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia

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