The mechanism shaping the logistic growth of mutation proportion in epidemics at population scale

Virus evolution is a common process of pathogen adaption to host population and environment. Frequently, a small but important fraction of virus mutations are reported to contribute to higher risks of host infection, which is one of the major determinants of infectious diseases outbreaks at population scale. The key mutations contributing to transmission advantage of a genetic variant often grow and reach fixation rapidly. Based on classic epidemiology theories of disease transmission, we proposed a mechanistic explanation of the process that between-host transmission advantage may shape the observed logistic curve of the mutation proportion in population. The logistic growth of mutation is further generalized by incorporating time-varying selective pressure to account for impacts of external factors on pathogen adaptiveness. The proposed model is implemented in real-world data of COVID-19 to capture the emerging trends and changing dynamics of the B.1.1.7 strains of SARS-CoV-2 in England. The model characterizes and establishes the underlying theoretical mechanism that shapes the logistic growth of mutation in population.