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.
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Partially supported by NSF Grant No. DMS-8703631. This work was done while this author was visiting the University of Victoria
Research supported in part by NSERC A-8965
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Busenberg, S., van den Driessche, P. Analysis of a disease transmission model in a population with varying size. J. Math. Biol. 28, 257–270 (1990). https://doi.org/10.1007/BF00178776
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DOI: https://doi.org/10.1007/BF00178776