Persistence under relaxed point-dissipativity (with application to an endemic model).

*(English)*Zbl 0774.34030The 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)