Analysis of a disease transmission model in a population with varying size
Date
2010-05-13T15:54:17Z
Authors
Busenberg, Stavros
Van den Driessche, P.
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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.
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Keywords
Epidemiological model, Endemic proportions, Global stability, Nonexistence of periodic solutions, Thresholds, Varying population