The stability of a mathematical model in the presence of a preventive vaccine

Abstract

Various kinds of deterministic models for the spread of infectious disease in populations have been analyzed mathematically and applied to specific diseases. In this paper a deterministic model for the dynamics of an infectious disease in the presence of a preventive vaccine is formulated. The model is a special case of a more general model, which is also applicable to other models of infectious diseases. The three dimensional model which assumes a non-linear incidence rate is analyzed qualitatively to determine the stability of its equilibria. This model is used to investigate the potential impact of the optimal vaccine coverage threshold needed for disease control and eradication