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A Global Stability Result and Existence and Uniqueness of Solution to an Age-Structured SI Epidemic Model with Disease-Induced Mortality and Vertical Transmission of Disease

M. El-Doma

Abstract


We prove the existence and uniqueness of solution to an SI age-structured epidemic model for a vertically as well as horizontally transmitted disease when the fertility, natural mortality and disease-induced mortality rates depend on age and the force of infection of proportionate mixing assumption type. We also show that solutions of the model equations depend continuously on the initial age-distributions; and that the trivial equilibrium is globally stable, if the net reproduction rate is less than one.

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