Fig 8. The effect of incomplete or imperfect vaccination (for μ = 10⁻⁹).

(a) When the proportion of unvaccinated people exceeds 1/R₀, such that herd immunity is not attained, the advantage of spatial vaccination is lost. (b) A similar outcome is achieved if the vaccine is not fully effective in preventing transmission (“leakage”). (c) If the vaccine’s effectiveness wanes over time, the advantage of spatial vaccination is lost for an intermediate rate of waning.