Distributed susceptibility: A challenge to persistence theory in infectious disease models

Horst Thieme

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider an S-I(-R) type infectious disease model where the susceptibles differ by their susceptibility to infection. This model presents several challenges. Even existence and uniqueness of solutions is non-trivial. Further it is difficult to linearize about the disease-free equilibrium in a rigorous way. This makes disease persistence a necessary alternative to linearized instability in the superthreshold case. Application of dynamical systems persistence theory faces the difficulty of finding a compact attracting set. One can work around this obstacle by using integral equations and limit equations making it the special case of a persistence theory where the state space is just a set.

Original languageEnglish (US)
Pages (from-to)865-882
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number4
StatePublished - Nov 2009


  • Compact attractor
  • Dynamical system
  • Epidemic model
  • Integral equation
  • Laplace transform
  • Limit solutions
  • Reproduction number
  • Semiflow
  • Translation invariance
  • Uniform persistence

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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