Rates of SARS-CoV-2 transmission and vaccination impact the fate of vaccine-resistant strains

Vaccines are thought to be the best available solution for controlling the ongoing SARS-CoV-2 pandemic. However, the emergence of vaccine-resistant strains may come too rapidly for current vaccine developments to alleviate the health, economic and social consequences of the pandemic. To quantify and characterize the risk of such a scenario, we created a SIR-derived model with initial stochastic dynamics of the vaccine-resistant strain to study the probability of its emergence and establishment. Using parameters realistically resembling SARS-CoV-2 transmission, we model a wave-like pattern of the pandemic and consider the impact of the rate of vaccination and the strength of non-pharmaceutical intervention measures on the probability of emergence of a resistant strain. As expected, we found that a fast rate of vaccination decreases the probability of emergence of a resistant strain. Counterintuitively, when a relaxation of non-pharmaceutical interventions happened at a time when most individuals of the population have already been vaccinated the probability of emergence of a resistant strain was greatly increased. Consequently, we show that a period of transmission reduction close to the end of the vaccination campaign can substantially reduce the probability of resistant strain establishment. Our results suggest that policymakers and individuals should consider maintaining non-pharmaceutical interventions and transmission-reducing behaviours throughout the entire vaccination period.

Impact of the rate of vaccination and initiation of low rate of transmission on model dynamics for p = 10 -7 . The cumulative death rate from the a, wildtype and b, resistant strains, c, the number of wildtype-strain infected individuals at t v60 , the point in time when 60% of the population is vaccinated and d, the probability of resistant strain establishment. e-g, Probability density that the resistant strain emerges as a function of time since the start of the simulation, t, rescaled by the time at which 60% of the individuals are vaccinated, t v60 , summed across simulations with θ (0.001 through 0.015), F h (2,000 through 20,000). The impact of the extraordinary low transmission period centered at t/t v60 = 1 on the likelihood of emergence of the resistant strain as a function of the duration of that period, T (colour-coded), and the intensity of the reduction of transmission e, β l = 0.055, f, β l = 0.03, g, β l = 0.01.

Figure S3
Impact of the rate of vaccination and initiation of low rate of transmission on model dynamics for p = 10 -8 . The cumulative death rate from the a, wildtype and b, resistant strains, c, the number of wildtype-strain infected individuals at t v60 , the point in time when 60% of the population is vaccinated and d, the probability of resistant strain establishment. e-g, Probability density that the resistant strain emerges as a function of time since the start of the simulation, t, rescaled by the time at which 60% of the individuals are vaccinated, t v60 , summed across simulations with θ (0.001 through 0.015), F h (2,000 through 20,000). The impact of the extraordinary low transmission period centered at t/t v60 = 1 on the likelihood of emergence of the resistant strain as a function of the duration of that period, T (colour-coded), and the intensity of the reduction of transmission e, β l = 0.055, f, β l = 0.03, g, β l = 0.01. Figure S4 The probability of establishment of the resistant strain for p = 10 -5 . The influence of low transmission period centered at t/t v60 = 1 on probability of establishment of the resistant strain as a function of the duration of that period, T, and the intensity of the reduction of transmission, β.

Figure S5
The probability of establishment of the resistant strain for p = 10 -6 . The influence of low transmission period centered at t/t v60 = 1 on probability of establishment of the resistant strain as a function of the duration of that period, T, and the intensity of the reduction of transmission, β.

Figure S6
The probability of establishment of the resistant strain for p = 10 -7 . The influence of low transmission period centered at t/t v60 = 1 on probability of establishment of the resistant strain as a function of the duration of that period, T, and the intensity of the reduction of transmission, β.

Figure S7
The probability of establishment of the resistant strain for p = 10 -8 . The influence of low transmission period centered at t/t v60 = 1 on probability of establishment of the resistant strain as a function of the duration of that period, T, and the intensity of the reduction of transmission, β.   Figure S11 Impact of the rate of vaccination and initiation of low rate of transmission on model dynamics for p = 10 -8 and exit from low transmission at F l =F h /8. The cumulative death rate from the a, wildtype and b, resistant strains, c, the number of wildtype-strain infected individuals at t v60 , the point in time when 60% of the population is vaccinated and d, the probability of resistant strain establishment. Figure S12. The fraction of surviving strains after T=200 days in 10 7 runs, first initialized with I wt = 200 infected individuals. The red dashed line shows the expected fraction of surviving strains, as computed with eq. 13. The stochastic algorithm becomes exact, if no Tau Leaping is employed and instead the whole simulation is evaluated using the Gillespie SSA scheme.