Analysis of a disease transmission model in a population with varying size |
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| Authors: | S Busenberg P van den Driessche |
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| Institution: | (1) Department of Mathematics, Harvey Mudd College, 91711 Claremont, CA, USA;(2) Department of Mathematics, University of Victoria, V8W 2Y2 Victoria, BC, Canada |
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| 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.Partially supported by NSF Grant No. DMS-8703631. This work was done while this author was visiting the University of VictoriaResearch supported in part by NSERC A-8965 |
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| Keywords: | Epidemiological model Endemic proportions Global stability Nonexistence of periodic solutions Thresholds Varying population |
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