Journal of Applied Mathematics 
Volume 2004 (2004), Issue 3, Pages 235-254
doi: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

M. El-Doma

 Faculty of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum 11115, Sudan
Received 30 January 2003; Revised 8 February 2004

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.