Fig. 3. Heatmaps depicting various epidemiological outcomes contingent on dosing regimes.

(A) Cumulative severe (left) and total (right) case numbers relative to the scenario with no vaccine from the time of vaccine introduction through the end of the 5-year time period after onset of the pandemic as a function of the one-dose to two-dose immune response ratio x_e and the interdose period. Parameters correspond to the weak immunity scenario of Fig. 2A, but x_e sets the value of ϵ₁, ρ₁, and $x_{\mathrm{sev},1}$. Specifically, we take ϵ₁ = ϵ₂ + (1 − x_e)(1 − ϵ₂) such that the susceptibility to infection after a waned single dose interpolates linearly between the value after waned two doses (ϵ₂) when the one- and two-dose immune responses are equally strong (x_e = 1) and unity (full susceptibility) when a single dose offers no immune protection (x_e = 0). Similarly, we take x_sev,1 = x_sev,2 + (1 – x_e)( x_sev,V – x_sev,2), such that the fraction of severe cases for infections after a waned single dose interpolates linearly between the value after waned two doses (x_sev,2) when x_e = 1 and the value after a (failed) vaccination x_sev,V when x_e = 0. Finally, ρ₁ is given by ρ₁ = ρ₂/x_e. (B) Values of ν_min, the minimal rate of first dose administration per day such that for any ν > ν_min the basic reproduction $R_0\left[\mathrm{\nu }\right]<1$ and the disease cannot invade (see supplementary materials), as a function of the strength of immunity after one (ϵ₁) and two (ϵ₂) waned vaccines doses, for different interdose periods. We take the duration of one-dose and two-dose vaccinal immunity to be 1/ρ₁ = 0.5 years and 1/ρ₂ = 1 year, respectively, and set ${ϵ}_{V_1}=0.1$ and ${ϵ}_{V_2}=0.05$.