Maximal Prevalence and the Basic Reproduction Number in Simple Epidemics

  • L. Esteva
  • K. P. Hadeler
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 126)


For the basic versions of the SIR and SIRS epidemic models estimates for the maximal prevalence are computed in terms of the basic reproduction number and other relevant quantities. Maximal prevalence is studied as a function of the rate of loss of immunity. Total size and total cost (total infected time) of the epidemic are estimated. For SIR models with demographic renewal it is investigated whether prevalence is a monotone function of the renewal rate.


Unstable Manifold Reproduction Number Epidemic Model Endemic Equilibrium Basic Reproduction Number 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • L. Esteva
    • 1
  • K. P. Hadeler
    • 2
  1. 1.Departamento de Matemáticas, Facultad de CienciasUNAMMéxico D.F.Mexico
  2. 2.BiomathematicsUniversity of TübingenTübingen

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