SARS-CoV-2 mutational cascades and the risk of hyper-exponential growth

The emergence of novel SARS-CoV-2 variants of concern (VOC), in late 2020, with selective transmission advantage and partial immunity escape potential, has been driving further evolution in the pandemic. The timing of mutational evolution and its limits are thus of paramount importance in preparedness planning. Here, we present a model predicting the pattern of epidemic growth including the emergence of variants through mutation. It is based on the SEIR (Susceptible, Exposed, Infected, Removed) model, but its equations are modified according to the transmission parameters of novel variants. Since more transmissible strains will drive a further increase in the number of cases, they will also lead to further novel mutations. As one cannot predict whether there is a viral mutational evolutionary limit, we model a cascade that could lead to hyper-exponential growth (HEG) involving the emergence of even more transmissible mutants that could overwhelm any systematic response. Our results are consistent with the timing, since the beginning of the pandemic, of the concurrent and independent emergence of the VOCs. The current dominance of the Delta variant and the need for additional public health measures indicates some of the risks of a possible HEG. We examine conditions that favor the expected appearance of similar variants, thus enabling better preparedness and more targeted research.