Abstract:
:We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
van den Driessche P,Yakubu AAdoi
10.1007/s11538-018-0426-2subject
Has Abstractpub_date
2019-11-01 00:00:00pages
4412-4446issue
11eissn
0092-8240issn
1522-9602pii
10.1007/s11538-018-0426-2journal_volume
81pub_type
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