The Impact of Imperfect Vaccination on Infectious Disease Transmission in an Age-Structured Population

Abstract

In this paper, we consider the influence of imperfect vaccination on the spread of infectious diseases in an age-structured population. The benefits of vaccination, even if not perfect, generally outweigh the risks of severe diseases. In a mathematical system, we consider the compartment of susceptible s; vaccinated v and infected i individuals with an age structure. The proposed model is globally analyzed by introducing total trajectories and employing a suitable Lyapunov functional. To illustrate our theoretical findings, we include numerical simulations at the end of the paper.

AMS subject classification: 35Q92, 37N25, 92D30.

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Communicated Editor: Boumediène Abdellaoui

Manuscript received Mar 09, 2024; revised Jan 05, 2025; accepted Jan 19, 2025; published Jan 23, 2025.