Fig 6. The effect of complete mass vaccination (i.e. p = 1) with vaccines of different properties on the infection dynamics in the case of continuous (left column) and one-off (right column) reactive vaccination.

Profiles of different colours correspond to different times when vaccination is applied, i.e. (i) at the start of the epidemic, equivalent to prophylactic vaccination (red continuous curves), (ii) at one quarter of the time of peak prevalence (green dotted curves), (iii) at one half of the time of peak prevalence (blue dotted curves), (iv) at the time of peak prevalence (red dotted curves), (v) at double the time until peak prevalence (gold dotted curves) and when (vi) vaccination is not applied at all (black continuous curves). A.-B. The vaccine only affects host susceptibility, i.e. sterilizing immunity, but no effect on infectivity or recovery (ϵ_s = 0.5, ϵ_γ = ϵ_i = 0) (see relations (7) and (10)); C.-D. The vaccine only speeds up recovery, but offers no protection from infection and no reduction in infectivity (ϵ_γ = 0.5, ϵ_s = ϵ_i = 0) (see Eqs (9) and (10)); E.-F. The vaccine equally affects host susceptibility, infectivity and recovery rate, ϵ = ϵ_s,i,γ = 0.5 (see Eqs (7)–(9) and (10)). Here β_NN = 0.12, γ_N = 0.01785, p = 1, d = 0.001, μ = 0.0017, and the initial conditions are S_N(0) = 0.999, I_N(0) = 0.001 (see relation (11) for p = 0 and I₀ = 0.001).