Fig. 1.

The basic model of waning immunity and self-boosting vaccination. (A) Schematic illustrating the model structure. All individuals die at a per-capita death rate μ, not shown in the diagram for clarity. (B) Dynamical behavior for a range of self-boosting rates, σ₁, assuming that mass vaccination acts from t = 1 onward. Although shown for a specific set of parameters (R₀ = 15, μ = 1/50, σ₀ = 0.1, γ = 17, P = 0.95), these curves illustrate the general, qualitative dynamics arising from the model shown in A.