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Stability Analysis for an SIR Age-Structured Epidemic Model with Vertical Transmission and Vaccination

M. El-Doma


An SIR age-structured epidemic model of a vertically as well as horizontally transmitted disease under vaccination is investigated when the total population in steady state, and the force of infection of proportionate mixing assumption type. We prove the existence and uniqueness of solution and show that the solutions of the model equations depend continuously on the initial agedistributions. We determine the steady states, and obtain explicitly
computable thresholds in terms of the demographic and epidemiological parameters of the model. We then perform stability analysis.

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