An extended SIR model with vaccine dynamics for SARS-CoV-2 adaptation rate

The COVID-19 pandemic is caused by infection with a SARS-CoV-2 virus, a RNA virus characterized by high mutation and replication rates. From epidemiological perspective, the trajectory in time of viral adaptation is determined by two opposite forces: (a) proportion of the population who has acquired immunity, exerting thereby a selective pressure on the virus and (b) proportion of infected people in the population, measuring the net viral load in the population. We calculate both the number of advantageous mutations in the population that have accumulated by time t and the amount of viral adaptation transmitted to a susceptible compartment, the latter being called the Evolutionary Infectivity Profile (EIP). To this end we employ first a simple compartmental SIR model with a single parameter describing reduction in transmission due to vaccination. Then we switch to a model which actuates the full vaccine dynamics, including vaccination rate and short duration of immunity. In our models we have never come across a situation where vaccination plays a dominant role in driving new SARS-CoV-2 variants. Nevertheless if the vaccination rate is not high enough, the EIP would continuously grow with time, pointing to a fruitful field for proliferation of genetically variable SARS-CoV-2 viruses.