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Uniform weak implies uniform strong persistence for nonautonomous semiflows. (English) Zbl 0918.34053
Summary: It is shown that, under two additional assumptions, uniformly weakly persistent semiflows are uniformly strongly persistent even if they are nonautonomous. 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.

34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
92D30 Epidemiology
37-XX Dynamical systems and ergodic theory
34D05 Asymptotic properties of solutions to ordinary differential equations
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