We derive a numerical model representing the emergence and evolution of SARS-CoV-2 variants, informed by data from in-vitro passaging experiments in Vero B4 Cells. We compare our numerical simulation results against probabilistic derivations of the expected probability of and time until the fittest variant becomes fixed in the population. Contrary to literature surrounding DNA viruses and eukaryotes where probabilities of fitness extremes are often modelled by exponential decaying tail, we show that above wildtype fitness differences for SARS-CoV-2 are actually best modelled by a heavy-tailed Fréchet distribution. Furthermore, we find that SARS-CoV-2 variants evolve through an essentially deterministic process rather than a diffusional one, with the dynamics driven by the fitness difference between the top variants rather than the sampling/dilution process. An interesting consequence of this setting is that the number of variant virions, rather than their proportion, is a better predictor of the probability of fixation of a variant.
Keywords: Branching processes; Extreme value theory; Fréchet; Numerical simulation; SARS-coV-2 fitness mutations; Viral mutation dynamics.
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