With the ongoing SARS-CoV-2 pandemic an issue of controlling the evolution and spread of novel variants is becoming very important. There are three main factors of particular epidemiological concern: higher infectivity, immunogenic drift (vaccine resistance), and increased virulence. Unless higher virulence comes together with higher infectivity (pleiotropy), higher virulence strains are not expected under the natural selection, we thus focus on the interplay of infectivity and vaccine resistance in this paper.

Vaccine Resistance Parameter Dependence © Yuliya Kulikova

So far we have seen a number of new strains that have emerged, with the most striking epidemiological factor of increased infectivity. Indeed, delta appears more infectious than the original strain, which has further been trumped by omicron. By contrast, vaccine escape of these new strains has not been as drastic, although still present.

The emergence of a new strain is an inherently stochastic process under the extensive influence of genetic drift. Therefore, it is important to model the dynamics of the new strains at their onset in a stochastic way to allow for genetic drift in the early phases of population dynamics of the new strains. We build a SIR-derived model (as in our previous work, Rella et al. 2021) with initial stochastic dynamics for the new strains to study the probability of their emergence and establishment. Our setup allows us to quickly assess the dynamics of emerging strains while maintaining the realism of the stochastic nature of population genetic processes that determine the fates of rare alleles in the population. At the same time, our setup allows testing the effect of vaccine hesitancy on the evolution of new strains and the effect of different non-pharmaceutical interventions to control the spread of the pandemic.

Which one of the two strains will win in the population? It is not a simple question because an emerging pandemic is not in an equilibrium state, with the number of infections coming in waves, the number of vaccinated and recovered people increasing over time, immunity vanishing over time, and different countries imposing different policies to control the spread of the pandemic. We study how infectivity, vaccine resistance, vaccination rates, and non-pharmaceutical interventions interact, affecting the selective advantage of different strains. Our main result is that until the virus reaches some higher limit of infectivity, vaccine-resistant variants will continue to be eliminated from the population.