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Journal of Applied Mathematics
Volume 2004 (2004), Issue 3, Pages 235-254
http://dx.doi.org/10.1155/S1110757X0430118X

Analysis of an age-dependent SI epidemic model with disease-induced mortality and proportionate mixing assumption: the case of vertically transmitted diseases

Faculty of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum 11115, Sudan

Received 30 January 2003; Revised 8 February 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An SI epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility, natural mortality, and disease-induced mortality rates depend on age and the force of infection corresponds to a special form of intercohort transmission called proportionate mixing. We determine the steady states and obtain explicitly computable threshold conditions, and then perform stability analysis.