Figure 3.

The function ℜ_v for scenario B of table 1 with a) proportional, and b) preferential, mixing. The dark blue planes represent ℜ_v = 1 and the lighter blue plane and curved (rainbow) surface represent ℜ_v for other tabulated parameters at all possible (p₁, p₂) pairs when a) ε₁ = ε₂ = 0 and b) ε₁ = ε₂ = 0.5, respectively. ℜ_v ≤ 1 for all combinations of p_i (i=1, 2) at or below the dark blue plane. While there is no single population-immunity threshold when n > 1, ℜ_v retains its utility as a threshold for outbreak prevention and, ultimately, disease elimination.