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

Stavros Busenberg | Zendy; P. van den Driessche | Zendy

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

Author(s) -

Stavros Busenberg,

P. van den Driessche

Publication year - 1990

Publication title -

journal of mathematical biology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.928

H-Index - 97

eISSN - 1432-1416

pISSN - 0303-6812

DOI - 10.1007/bf00178776

Subject(s) - population size , transmission (telecommunications) , population , mathematics , population model , statistical physics , biology , statistics , econometrics , biological system , demography , computer science , physics , telecommunications , sociology

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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