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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniform weak implies uniform strong persistence for non-autonomous semiflows


Author: Horst R. Thieme
Journal: Proc. Amer. Math. Soc. 127 (1999), 2395-2403
MSC (1991): Primary 34C35, 34D05, 92D30
Published electronically: April 15, 1999
MathSciNet review: 1622989
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Abstract: 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.


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Additional Information

Horst R. Thieme
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804
Email: h.thieme@asu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05034-0
PII: S 0002-9939(99)05034-0
Received by editor(s): November 10, 1997
Published electronically: April 15, 1999
Additional Notes: The author’s research was partially supported by NSF grant DMS-9403884.
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society