  Cancer is a complex disease and thus is complicated to model. However, simple
models that describe the main processes involved in tumoral dynamics, e.g.,
competition and mutation, can give us clues about cancer behaviour, at least
qualitatively, also allowing us to make predictions. Here we analyze a
simplified quasispecies mathematical model given by differential equations
describing the time behaviour of tumor cells populations with different levels
of genomic instability. We find the equilibrium points, also characterizing
their stability and bifurcations focusing on replication and mutation rates. We
identify a transcritical bifurcation at increasing mutation rates of the tumor
cells population. Such a bifurcation involves an scenario with dominance of
healthy cells and impairment of tumor populations. Finally, we characterize the
transient times for this scenario, showing that a slight increase beyond the
critical mutation rate may be enough to have a fast response towards the
desired state (i.e., low tumor populations) during directed mutagenic
therapies.
