Minimal seroprevalence achieved with heterogeneous distribution of vaccine.

With a flight-line spacing of 0.5 km, 0.013 ≤ κ ≤ 0.13 corresponds to host home ranges between 1 km2 and 10 km2. Vaccine distribution is tightly clustered (ξ = 0.025 km). Blue indicates seroprevalence values that exceed the 0.5 threshold required for herd immunity, red indicates values that do not. Other parameters: d = 0.416 yr−1, σ = 0.24 yr−1, δv = 12 yr−1.