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.2021 Jul 30;11(1):15729.
doi: 10.1038/s41598-021-95025-3.

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

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

Simon A Rella et al. Sci Rep..

Abstract

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.

© 2021. The Author(s).

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
The states, transition parameters and dynamics. (a) States are shown in circles and transition parameters in squares. The transition parameter,μ, is the rate at which individuals lose natural immunity andp, is the probability that an individual infected with the wildtype strain transmits a resistant strain, so it is not a deterministic parameter. Example dynamics of the number of individuals infected with the wildtype (blue) and resistant strains (red) forp = 10–6, θ0 = 1/365 and Fh = 15,000. The period of vaccination is highlighted (green). Under the same parameters the resistant strain may emerge and go extinct, (b), or become established, (c).
Figure 2
Figure 2
Impact of the rate of vaccination,θ, and the initiation of low rate of transmission,Fh, on model dynamics. The cumulative death rate from the (a) wildtype and (b) resistant strains, (c) the number of wildtype-strain infected individuals attv60, the point in time when 60% of the population is vaccinated and (d) the probability of resistant strain establishment, forp = 10–6. (e) The probability of emergence of the resistant strain as a function of the probability of emergence, p shown for the parameter ranges ofθ andFh in the corresponding red and blue boxes from figure (d). (f) The average number of times of 8 × 106 simulation runs during which a resistant strain emerges (black) or goes extinct (grey) during periods of low (βl) or high (βh) transmission forp = 10–6. (g) A resistant strain was never observed to establish during periods of low transmission (βl) for p = 10–6.
Figure 3
Figure 3
Time of initial emergence of a resistant strain that has become established. 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,tV60, averaged across simulations withθ (0.001 through 0.015),Fh (2000 through 20,000) andp = 10–6. Without any extraordinary periods of low transmission (blue line) the peak of the likelihood of emergence of a new strain is att/tV60 = 1. The likelihood of emergence of a resistant strain can be reduced by an extraordinary period of low transmission centered att/tV60 = 1 with a stronger reduction when such period is longer,T (colour-coded), or when the rate of transmission is more strongly reduced (a)βl = 0.055, (b)βl = 0.03, (c)βl = 0.01.
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