Fig 4. Integration of the ODEs on three toy genotype networks—The chain, square lattice and star—All with 25 strains.

We fix the recovery rate γ = 1, the mutation rate μ = 1/100, the waning immunity rate α = 1/50 and vary the transmission rate β under three values of transcending immunity: Δ = 5 (Left), Δ = 10 (Center), and Δ = 50 (Right). Close to the inflection point of every I* curve (shown in solid lines) we find a maximum in R* (shown in dashed lines). This point therefore marks a second activation threshold, one where the transmission rate is high enough to counteract transcending immunity and spread the outbreak using the pool of recovered individuals.