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

✍ Scribed by S. Busenberg; P. Driessche

Publisher
Springer
Year
1990
Tongue
English
Weight
727 KB
Volume
28
Category
Article
ISSN
0303-6812

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✦ Synopsis

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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The prevalence of Toxoplasmosis has increased dramatically around the world. Despite congenital Toxoplasmosis being not a disease of epidemic proportions, a large number of humans die or have serious effects on the developing fetus. In this paper we present an initial model with varying size populat