| Abstract: |
| In this study, we propose an SIRS-type epidemiological model incorporating imperfect vaccination, waning vaccine-induced immunity, and periodic revaccination. Vaccinated individuals are structured by the time elapsed since their last dose, leading to a vaccination-age dependent PDE coupled to an ODE system for the remaining compartments. A discrete-time formulation yields a high-dimensional ODE model consistent with the continuous description.
We analyze the equilibria and stability properties of both formulations and derive the basic reproduction number. The model exhibits backward bifurcations and bistability induced by waning immunity and revaccination, implying that disease persistence may occur even when the reproduction number is below one. Numerical continuation is used to investigate the influence of revaccination schedules and contact reduction measures. The results underline the structural role of immunity loss and demonstrate the necessity of combined vaccination and contact control strategies. |
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