Persistence under relaxed point-dissipativity (with application to an endemic model). (English) Zbl 0774.34030

Thieme, Horst R.

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)

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