Journal Article

A Kermack–McKendrick model applied to an infectious disease in a natural population

M. G. ROBERTS

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 16, issue 4, pages 319-332
Published in print December 1999 | ISSN: 1477-8599
Published online December 1999 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/16.4.319
A Kermack–McKendrick model applied to an infectious disease in a natural population

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The dynamics of a fatal infectious disease in a population regulated by density-dependent constraints are represented as a system of nonlinear integral equations. Survival probabilities and disease transmission coefficients may vary with the time elapsed since infection, and horizontal and vertical modes of transmission are allowed for. Criteria for the existence and stability of steady states are derived, and an example based on the dynamics of tuberculosis is presented. Finally, the relative merits of this approach, and the familar compartmental models based on differential equations are discussed.

Keywords: epidemic models; Kermack–McKendrick model; tuberculosis

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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