  It is well known that, during replication, RNA viruses spontaneously generate
defective viral genomes (DVGs). DVGs are unable to complete an infectious cycle
autonomously, and depend on coinfection with a helper wild-type virus (HV) for
their replication and/or transmission. The study of the dynamics arising from a
HV and its DVGs has been a longstanding question in virology. It has been shown
that DVGs can modulate HV replication and, depending on the strength of
interference, result in HV extinctions or self-sustained persistent
fluctuations. Extensive experimental work has provided mechanistic explanations
for DVG generation and compelling evidences of HV-DVGs virus coevolution. Some
of these observations have been captured in mathematical models. Here, we
develop and investigate an epidemiological-like mathematical model specifically
designed to study the dynamics of betacoronavirus in cell cultures experiments.
The dynamics of the model is governed by several degenerate normally hyperbolic
invariant manifolds given by quasineutral planes - i.e. filled by equilibrium
points. Three different quasineutral planes have been identified depending on
parameters and involving: (i) persistence of HV and DVGs; (\emph{ii})
persistence of non-infected cells and DVG-infected cells; and (iii) persistence
of DVG-infected cells and DVGs. Sensitivity analyses indicate that model
dynamics largely depend on the maximum burst size ($B$), and both the
production rate ($\beta$) and replicative advantage ($\delta$) of DVGs.
Finally, the model has been fitted to single-passage experimental data using
artificial intelligence and key virological parameters have been estimated.
