Mathematical model of replication–mutation dynamics in coronaviruses

RNA viruses are known for their fascinating evolutionary dynamics, characterised by high mutation rates, fast replication, and ability to form quasispecies - clouds of genetically related mutants. Fast replication in RNA viruses is achieved by a very fast but error-prone RNA-dependent RNA polymerase (RdRP). High mutation rates are a double-edged sword: they provide RNA viruses with a mechanism of fast adaptation to a changing environment or host immune system, but at the same time they pose risk to virus survivability in terms of either virus population being dominated by mutants (error catastrophe), or extinction of all viral sequences due to accumulation of mutations (lethal mutagenesis). Coronaviruses, being a subset of RNA viruses, are unique in having a special enzyme, exoribonuclease (ExoN), responsible for proofreading and correcting errors induced by the RdRP. In this paper we consider replication dynamics of coronaviruses with account for mutations that can be neutral, deleterious or lethal. Compared to earlier models of replication of RNA viruses, our model also explicitly includes ExoN and its effects on mediating viral replication. Special attention is paid to different virus replication modes that are known to be crucial for controlling the dynamics of virus populations. We analyse extinction, mutant-only and quasispecies steady states, and study their stability in terms of different parameters, identifying regimes of error catastrophe and lethal mutagenesis. With coronaviruses being responsible for some of the largest pandemics in the last twenty years, we also model the effects of antiviral treatment with various replication inhibitors and mutagenic drugs.