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Uniform persistence and permanence for non-autonomous semiflows in population biology. (English) Zbl 0970.37061
The author proves that under certain additional conditions uniform weak persistence implies uniform strong persistence. Then he shows how persistence theory can be turned around to demonstrate ultimate boundedness (or point dissipativity) for non-autonomous semiflows. Finally, these results are applied to establish threshold criteria for disease extinction and disease persistence in time heterogeneous SIRS epidemic models and to establish permanence for a one species model consisting of a scalar retarded functional-differential equation.

MSC:
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
92D30 Epidemiology
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
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