An allele-based evolution model of the population spread of SARS-CoV-2

We present and analyze a dynamic evolution-oriented model of the spread of SARS-CoV-2 in a (homogeneous) population. Unlike previous such models, we use alleles at the various virus sites as our basic building blocks - an approach that we find more natural and more effective in studying the evolution of viral strains. Our model parameters include: transmissibility, immunity levels, immunity waning rates, residual waned immunity levels, infection duration, mutation rates, epistasis, and possible antibody dependent enhancement. To compensate for the model complexity required for all of these features, we restrict to two virus sites with two alleles at each site, allowing us to explore how each of these features interacts with the basic evolutionary processes involved in viral strain changes. Our results show several qualitative patterns of interest in understanding viral strain dynamics, including founder effects of the seeded strain and an interplay between ease of evolution to neighboring strains and immune advantages of complementary strains. Overall, our allele-based approach uncovers insights about virus evolution, including the effects of parameter choices on the timing and patterns of the evolution of new strains, the staying power of the initial (seeded) strain, and the key roles that immunity plays. Author SummaryWe developed an allele-based model of pathogen evolution, coupled with a population-based transmission model that captures a variety of susceptibility, infectiousness, and immune effects. Instead of describing viruses only by their "strain," as most other population-based models do, we represent them through their genetic components--alleles--that shape transmissibility and immune escape. This approach provided a natural way to model how new variants arise through mutation and how population immunity influences their success. Our default model had the seeded strain and its complement (with opposing mutations at both sites in the simplified 2-site 4-strain model we examine here) dominating the pandemic. We examined how the appearance of strains with alleles with different properties would affect this pattern. In some cases, there was minimal effect, e.g., changes in the mutation rate or in the residual immunity after waning; in other cases, e.g., longer infection duration or faster waning immunity, new strains came to dominate. By coupling allele-level dynamics with epidemiological processes, we hope this work begins to bridge laboratory and population scales.