Please join us welcoming Ph.D student Ginelle Gonzalez for this week's graduate student seminar.  

Our Graduate Student Seminar gives students the ability to showcase interesting results that they have found in their research. Presenters are typically graduate students in mathemathematics, but can also be undergraduates, students in other disiplines, and faculty as well. 

Presentations should be able to be understood by undergraduate students in mathematics or related disipline. 

Abstract: Systems of differential equations can be used to model populations of various cell types in the human body. A mathematical model observing the immune, normal, and tumor cell interactions is presented in this paper. Our main objective is to perform stability and bifurcation analysis on this model. After introducing and removing different terms and parameters from an existing model, our observations revealed vital cell behaviors in the body depending on the patient's biological attributes. Analysis of the system's stability and bifurcations around its equilibrium points is carried out to observe the behavior of three distinct cases: cured, deceased, and coexistence. We add a crowding sensitivity parameter, m, to the tumor equation and remove a term from the immune cell equation in our system. We found that Hopf bifurcations arise when changing our competition parameters from destructive to advantageous and changing our crowding parameter from insensitive to sensitive.