a counterintuitive result of our analysis is that the highest risk of resistant strain establishment occurs when a large fraction of the population has already been vaccinated but the transmission is not controlled.


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.


Our model suggests three specific risk factors that favour the emergence and establishment of a vaccine-resistant strain that are intuitively obvious: high probability of initial emergence of the resistant strain, high number of infected individuals54 and low rate of vaccination55. By contrast, a counterintuitive result of our analysis is that the highest risk of resistant strain establishment occurs when a large fraction of the population has already been vaccinated but the transmission is not controlled. Similar conclusions have been reached in a SIR model of the ongoing pandemic56 and a model of pathogen escape from host immunity57. Furthermore, empirical data consistent with this result has been reported for influenza58. Indeed, it seems likely that when a large fraction of the population is vaccinated, especially the high-risk fraction of the population (aged individuals and those with specific underlying conditions) policy makers and individuals will be driven to return to pre-pandemic guidelines59 and behaviours conducive to a high rate of virus transmission60,61. However, the establishment of a resistant strain at that time may lead to serial rounds of resistant strain evolution with vaccine development playing catch up in the evolutionary arms race against novel strains.

Prior to discussion of the implications of our model we reflect on several properties of the assumptions and implementation of our model. In classical SIR-like deterministic models even a single individual infected with a vaccine resistant strain with reproduction number Rt > 1 will lead to automatic establishment of the strain in the population. In an analytical solution, a SIR-like model, even for Rt < 1 for the vaccine resistant strain, the number of infected individuals will tend to 0 but only as time tends to infinity. In actual populations, a single individual infected with a vaccine resistant strain still has a non-negligible chance not to infect anyone causing the variant to go extinct due to random stochastic forces47. Therefore, the implementation of stochastic dynamics62,63 of the vaccine resistant strain at low frequency in our model, considers the impact of random drift on its dynamics, which lies at the heart of extinction of rare strains.

We considered the dynamics of a single vaccine resistant strain, however, there may be different mutations that can lead to vaccine resistance. The emergence of different genotypes causing the same phenotype is analogous to a distinction in population genetics between alleles identical by state and by descent64. In our model, the treatment of independent emergence of different mutations as a single entity does not influence the dynamics under the following two assumptions. First, that different mutations lead to exactly the same phenotype, which is vaccine resistance, and, second, that there is no recombination. However, the reported dynamics may be quantitatively different if either of the two assumptions do not hold.

We have not explored the parameter ranges of βh, βl, the high and low rates of transmission, respectively, and Fl the threshold between low and high rate of transmission. We selected the βh and βl, to represent the known transmission values at the start of the pandemic31,32,33. However, evolving strains are reported to have a higher rate of transmission10 leading to higher βh and, possibly, βl values than we used. An increase in the rate of transmission is not expected to qualitatively influence the reported dynamics, but would shift the probability density of establishment of a resistant strain (Fig. 3). Indeed, the peak probability at 60% vaccinated individuals roughly corresponds to the point at which for the given βh, Rt, the average number of transmissions for one infected individual, becomes less than 1. Because the reproduction number for the vaccine resistant strain, Rt, is equal to (S + V)β/N(γ + δ), the perk of the risk of establishment of the vaccine resistant strain would increase proportional to an increase of β. An increase in either Fh or Fl would lead to more individuals becoming infected and a proportionally higher rate of emergence of the vaccine related strain, but would not change the qualitative behaviour of the model. Furthermore, an increase of Fl would lead to reversion to a high transmission rate with higher number of infected individuals, leading to shorter periods of low transmission and decreased probability of extinction of the vaccine resistant strains.

The results of our model provide several qualitative implications for the strategy forward in the months of vaccination. In our model, the probability of emergence of a resistant strain in one individual per day was in the range of 105 to 108 for a population of 107 individuals. For the entire human population of ~ 1010 that probability would be 108 to 1011, which does not seem improbably large. As of February 2021, ~ 109 individuals have been infected by SARS-CoV-265 with an average 14 days of sickness per individual25, so > 1010 number of total days of infected individuals. Furthermore, highly mutated strains may emerge as a result of long shedding in immunocompromised individuals, a rare but realistic scenario66,67,68. Taken together, the emergence of a partially or fully vaccine-resistant strain and its eventual establishment appears inevitable. However, as vaccination needs to be ahead of the spread of such strains in similar ways to influenza23, it is necessary to reduce the probability of establishment by a targeted effort to reduce the virus transmission rate towards the end of the vaccination period before the current vaccines become ineffective. Conversely, lack of non-pharmaceutical interventions at that time can increase the probability of establishment of vaccine-resistant strains. For example, plans to vaccinate individuals with a high risk of a fatal disease outcome followed by a drive to reach herd immunity while in uncontrolled transmission among the rest of the population is likely to greatly increase the probability that a resistant strain is established, annulling the initial vaccination effort. Another potential risk factor may be the reversion of vaccinated individuals to pre-pandemic behaviours that can drive the initial spread of the resistant strain.

One simple specific recommendation is to keep transmission low even when a large fraction of the population has been vaccinated by implementing acute non-pharmaceutical interventions (i.e. strict adherence to social distancing) for a reasonable period of time, to allow emergent lineages of resistant strains to go extinct through stochastic genetic drift. The implementation of non-pharmaceutical measures at a time of high vaccination can also help reduce infectivity when the efficacy of vaccines is not perfect69. Additional factors that may make these measures even more effective are: (1) increased and widespread testing, (2) rigorous contact tracing, (3) high rate of viral sequencing of positive cases58,70 and (4) travel restrictions. Finally, while our model formally considers only one homogenous population, our data also suggest that delays in vaccination in some countries relative to others will make the global emergence of a vaccine-resistant strain more likely. Without global coordination, vaccine resistant strains may be eliminated in some populations but could persist in others. Thus, a truly global vaccination effort may be necessary to reduce the chances of a global spread of a resistant strain.

DOI https://doi.org/10.1038/s41598-021-95025-3

Reprinted for educational purposes and social benefit, not for profit.