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Analysis of a disease transmission model in a population with varying size

Analysis of a disease transmission model in a population with varying size An S → I → R → S epidemiological model with vital dynamics in a population of varying size is discussed. A complete global analysis is given which uses a new result to establish the nonexistence of periodic solutions. Results are discussed in terms of three explicit threshold parameters which respectively govern the increase of the total population, the existence and stability of an endemic proportion equilibrium and the growth of the infective population. These lead to two distinct concepts of disease eradication which involve the total number of infectives and their proportion in the population. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Biology Springer Journals

Analysis of a disease transmission model in a population with varying size

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References (21)

Publisher
Springer Journals
Copyright
Copyright © 1990 by Springer-Verlag
Subject
Mathematics; Mathematical and Computational Biology; Applications of Mathematics
ISSN
0303-6812
eISSN
1432-1416
DOI
10.1007/BF00178776
Publisher site
See Article on Publisher Site

Abstract

An S → I → R → S epidemiological model with vital dynamics in a population of varying size is discussed. A complete global analysis is given which uses a new result to establish the nonexistence of periodic solutions. Results are discussed in terms of three explicit threshold parameters which respectively govern the increase of the total population, the existence and stability of an endemic proportion equilibrium and the growth of the infective population. These lead to two distinct concepts of disease eradication which involve the total number of infectives and their proportion in the population.

Journal

Journal of Mathematical BiologySpringer Journals

Published: Jul 6, 2004

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