Almost all viruses, regardless of their genomic material, produce defective
viral genomes (DVG) as an unavoidable byproduct of their error-prone
replication. Defective interfering (DI) elements are a subgroup of DVGs that
have been shown to interfere with the replication of the wild-type (WT) virus.
Along with DIs, other genetic elements known as satellite RNAs (satRNAs), that
show no genetic relatedness with the WT virus, can co-infect cells with WT
helper viruses and take advantage of viral proteins for their own benefit.
These satRNAs have effects that range from reduced symptom severity to enhanced
virulence. The interference dynamics of DIs over WT viruses has been thoroughly
modelled at within-cell, within-host, and population levels. However, nothing
is known about the dynamics resulting from the nonlinear interactions between
WT viruses and DIs in the presence of satellites, a process that is frequently
seen in plant RNA viruses and in biomedically relevant pathosystems like
hepatitis B virus and its δ satellite. Here, we look into a
phenomenological mathematical model that describes how a WT virus replicates
and produces DIs in presence of a satRNA at the intra-host level. The WT virus
is subject to mechanisms of complementation, competition, and various levels of
interference from DIs and the satRNA. Examining the dynamics analytically and
numerically reveals three possible stable states: (i) full extinction, (ii)
satellite extinction and virus-DIs coexistence and (iii) full coexistence.
Assuming DIs replicate faster than the satRNA owed to their smaller size drives
to scenario (ii), which implies that DIs could wipe out the satRNA. In
addition, a small region of the parameter space exists wherein the system is
bistable (either scenarios (ii) or (iii) are concurrently stable).Comment: 22 pages, 9 figure