Resumo:
We often use mathematical models to understand the dynamics of natural phenomena
and to study the behavior of diseases, such as Acute Promyelocytic Leukemia (APL).
APL is a subtype of Acute Myeloid Leukemia (AML) in which the bone marrow cannot
produce enough normal blood cells due to blockages in the maturation of these cells. This
dissertation presents a global analysis of a two-parameter family of polynomial vector
fields in the plane that models a simplified version of the dynamics of APL. All possible
local and global bifurcations are analyzed, and, using Poincaré compactification, complete
descriptions of their dynamics on the Poincaré disk are provided.
