  This article deals with an autonomous differential equation model that
studies the interaction between the immune system and the growth of tumor cells
with strong and weak Allee effects. The Allee effect refers to interspecific
competition, and when the population is small, it can retard population growth.
The work focuses on describing analytically, using a set of parameters, the
conditions in the phases of the immunoediting theory, particularly in the
equilibrium phase, where a latent tumor would exist. Saddle-Node,
Saddle-symmetric, Hopf, generalized Hopf, and Takens-Bogdanov bifurcations get
presented for both Allee effects, and their biological interpretation regarding
cancer dynamics gets discussed. The Hopf and generalized Hopf bifurcation
curves get analyzed through hyper-parameter projections of the model, where it
gets observed that with a strong Allee effect, more tumor control persists as
it has higher antigenicity, in contrast to the weak Allee effect, where lower
antigenicity gets observed. Also, we observe that the equilibrium phase
persists as antigenicity increases with a strong Allee effect. Finally, the
numerical continuation gets performed to replicate the analytical curves'
bifurcations and draw the limit and double limit cycles.
