Extended Data Fig. 9: The probability of a vaccine-resistant mutant increases dramatically when assuming waning of immunity and no booster vaccination, but is equivalent to the probability given by the basic model when booster vaccination is administered after 180 days.

In recent months, the waning of immunity conferred by vaccination or recovery has emerged as a concern as many individuals suffered breakthrough infections even after having been fully vaccinated. In response, some countries such as Israel have responded by launching a booster vaccination campaign for individuals that had been vaccinated more than five months prior. In this Figure, we show the probability of emergence of a vaccine resistant mutant simulated with the basic model, the extended model incorporating the waning of immunity but no booster vaccination (see Supplementary Fig. 14) and the extended model incorporating both the waning of immunity and the booster vaccination (see Supplementary Fig. 15). We observe that a booster vaccination campaign reduces the probability of emergence of a vaccine resistant mutant to that observed with the basic model. In contrast, if no booster vaccination is administered, the probability of emergence of the vaccine resistant mutant increases dramatically. This is especially true for high c values. When c is high, all the population is vaccinated within a short time frame. For c = 10,000 and L = 500, herd immunity is achieved within approximately two months. Since booster vaccination begins after 180 days, most vaccinated individuals will already be in the waned susceptible category, which means that they can get reinfected, thus increasing the probability of emergence of a vaccine resistant mutant. Parameters: N = 10⁶; a = 0.25; d = 0.01; μ = 10⁻⁶; q = 1; s₀ = 0.1, β₁ = β₂ = 7.5 ∙ 10⁻⁷. Error bars are calculated as in Extended Data Figure 2, and the number of runs is n=1000.