Sword of Damocles or choosing well. Population genetics sheds light into the future of the COVID-19 pandemic and SARS-CoV-2 new mutant strains.

An immense scientific effort has been made worldwide due to Covid-19s pandemic magnitude. It has made possible to identify almost 300,000 SARS-CoV-2 different genetic variants, connecting them with clinical and epidemiological findings. Among this immense data collection, that constitutes the biggest evolutionary experiment in history, is buried the answer to what will happen in the future. Will new strains, more contagious than the current ones or resistant to the vaccines, arise by mutation? Although theoretic population genetics is, by far, the most powerful tool we have to do an accurate prediction, it has been barely used for the study of SARS-CoV-2 due to its conceptual difficulty. Having in mind that the size of the SARS-CoV-2 population is astronomical we can apply a discrete treatment, based on the branching process method, Fokker-Plank equations and Kolmogoroffs forward equations, to calculate the survival likelihood through time, to elucidate the likelihood to become dominant genotypes and how long will this take, for new SARS-CoV-2 mutants depending on their selective advantage. Results show that most of the new mutants that will arise in the SARS-CoV-2 meta-population will stay at very low frequencies. However, some few new mutants, significantly more infectious than current ones, will still emerge and become dominant in the population favoured by a great selective advantage. Far from showing a "mutational meltdown", SARS-CoV-2 meta-population will increase its fitness becoming more infective. There is a probability, small but finite, that new mutants arise resistant to some vaccines. High infected numbers and slow vaccination programs will significantly increase this likelihood.