Uniform weak implies uniform strong persistence for non-autonomous semiflows

Thieme, Horst

doi:10.1090/S0002-9939-99-05034-0

Uniform weak implies uniform strong persistence for non-autonomous semiflows
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by Horst R. Thieme PDF

Proc. Amer. Math. Soc. 127 (1999), 2395-2403 Request permission

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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