Abstract
Conditions are presented for uniform strong persistence of non-autonomous semiflows, taking uniform weak persistence for granted. Turning the idea of persistence upside down, conditions are derived for non-autonomous semiflows to be point-dissipative. These results are applied to time-heterogeneous models of S-I-R-S type for the spread of infectious childhood diseases. If some of the parameter functions are asymptotically almost periodic, an almost sharp threshold result is obtained for uniform strong endemicity versus extinction in terms of asymptotic time averages. Applications are also presented to scalar retarded functional differential equations modeling one species population growth. (C) Elsevier Science Inc.
Original language | English (US) |
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Pages (from-to) | 173-201 |
Number of pages | 29 |
Journal | Mathematical Biosciences |
Volume | 166 |
Issue number | 2 |
DOIs | |
State | Published - 2000 |
Keywords
- (Asymptotically) almost periodic functions
- Dissipativity
- Dynamical systems
- Epidemic models
- Functional differential equations
- Permanence
- Persistence
- Time averages
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Agricultural and Biological Sciences
- Applied Mathematics