Abstract
Several mathematical models in SARS-CoV-2 have shown how target-cell model
can help to understand the spread of the virus in the host and how potential
candidates of antiviral treatments can help to control the virus. Concepts as
equilibrium and stability show to be crucial to qualitatively determine the
best alternatives to schedule drugs, according to effectivity in inhibiting the
virus infection and replication rates. Important biological events such as
rebounds of the infections (when antivirals are incorrectly interrupted) can
also be explained by means of a dynamic study of the target-cell model. In this
work, a full characterization of the dynamical behavior of the target-cell
models under control actions is made and, based on this characterization, the
optimal fixed-dose antiviral schedule that produces the smallest amount of dead
cells (without viral load rebounds) is computed. Several simulation results -
performed by considering real patient data - show the potential benefits of
both, the model characterization and the control strategy.