Uniform Weak Implies Uniform Strong Persistence for Non-autonomous Semiflows

@inproceedings{Thieme1999UniformWI,
  title={Uniform Weak Implies Uniform Strong Persistence for Non-autonomous Semiflows},
  author={Horst R. Thieme},
  year={1999}
}
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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