Uniform weak implies uniform strong persistence for non-autonomous semiflows

Horst Thieme

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


It is shown that, under two additional assumptions, uniformly weakly persistent semiflows are also uniformly strongly persistent even if they are non-autonomous. This result is applied to a time-heterogeneous model of S-I-R-S type for the spread of infectious childhood diseases. If some of the parameter functions are almost periodic, an almost sharp threshold result is obtained for uniform strong endemicity versus extinction.

Original languageEnglish (US)
Pages (from-to)2395-2403
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number8
StatePublished - 1999

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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