Thieme, Horst R. Persistence under relaxed point-dissipativity (with application to an endemic model). (English) Zbl 0774.34030 SIAM J. Math. Anal. 24, No. 2, 407-435 (1993). The purpose of the paper is twofold: First the author provides sufficient conditions under which in a general dynamical system uniform weak persistence implies uniform strong persistence under relaxed point- dissipativity especially when it is only required in a neighborhood of the boundary. Second he illustrates his abstract approach by applying it to an epidemic model describing the spread of an infections disease in a population that would grow exponentially without the disease. In particular sufficient conditions are established for the disease and/or the host population to persist, as well as for the disease to limit the growth of the population. Reviewer: G.Karakostas (Ioannina) Cited in 256 Documents MSC: 37-XX Dynamical systems and ergodic theory 92D30 Epidemiology Keywords:dynamical system; uniform strong persistence under relaxed point- dissipativity; epidemic model; spread of an infections disease; growth of the population PDF BibTeX XML Cite \textit{H. R. Thieme}, SIAM J. Math. Anal. 24, No. 2, 407--435 (1993; Zbl 0774.34030) Full Text: DOI