Extended Data Fig. 7: Probability of emergence of resistance against a two-gene vaccine or for a two-step escape mutant.

For each combination of L (the number of allowed infections per day), c (the number of new vaccinations per day), and µ (the mutation rate), we simulate 1000 runs of the basic model (see Fig. 2 of the main text) and of the two-gene model (see Supplementary Fig. 12). We record the probability of emergence of vaccine resistance as the proportion of runs where we observed takeover of the vaccine resistant strain. The basic model assumes that the administered vaccine provides immunity against one viral antigen. Hence, it most closely corresponds to a “one gene vaccine”, and resistance can be acquired by the emergence of one mutation. In the two-gene model, we assume that the vaccine provides immunity to two independent viral antigens. Hence, two mutations are needed to give rise to resistance. In the one gene vaccine case, the probability of emergence of vaccine resistance is never negligible except for low mutation rate (μ = 10⁻⁶), low number of new infections per day (L = 100) and high vaccination rates (c = 10,000). In all cases, for high mutation rates, emergence of vaccine resistance is almost certain. For lower mutation rates, emergence of vaccine resistance is probable. However, in the case of a two-gene vaccine, we never observe emergence of vaccine resistance except for mutation rates higher than 10⁻⁴. Given our estimate of the upper bound of the mutation rate from wild type to vaccine resistant mutant, we can conclude that a two-gene vaccine would prevent the emergence of vaccine resistance for all combinations of L and c for realistic mutation rates. Parameters: N = 10⁶; a = 0.25; d = 0.01; s₀ = 0.1, β₁ = β₂ = 7.5 ∙ 10⁻⁷. Error bars are calculated as in Extended Data Figure 1, and the number of runs is n=1000.