Fig. 5: Estimating the mutation rate given that no vaccine-resistant mutant has taken over.

a, Using equation (2), we calculate the probability that an MT strain would have taken over by 30 July 2020. To this aim, we used the numbers of new infections and immunized individuals (needed to calculate R_MT at each time point) from OWID¹. The probability of MT strain takeover follows a sigmoidal function, where the midpoint is reached for the value of µ at which MT strain takeover becomes more probable than not. We consider this value of µ the upper bound of the mutation rate. For the United States, the estimated upper bound of the mutation rate on 30 July 2020 would be about 10⁻⁶ (red arrow). b, Using equation (2), we calculate the probability that an MT strain would have taken over by 29 November 2021. We observe that the curves describing the probability of takeover of the MT strain along the mutation rate have shifted left. This is because since 30 July 2020, additional cases have occurred without an MT strain takeover. The upper bound of the mutation rate therefore decreases. For the United States, the upper bound would now be estimated at 2 × 10⁻⁷ (red arrow). c, The midpoint of the function (the red arrows shown in a and b) describing the probability of MT strain takeover decreases in value as more time passes without takeover of an MT strain. We use this value as an upper bound of the mutation rate for our model.