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Full-Text Articles in Dynamical Systems
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
All HMC Faculty Publications and Research
In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …
Dynamic Equations On Changing Time Scales: Dynamics Of Given Logistic Problems, Parameterization, And Convergence Of Solutions, Kelli J. Hall
Dynamic Equations On Changing Time Scales: Dynamics Of Given Logistic Problems, Parameterization, And Convergence Of Solutions, Kelli J. Hall
Theses, Dissertations and Capstones
In this thesis we use the theory of dynamic equations on time scales to understand the changes in dynamics between difference and differen- tial equations by parameterizing the underlying domains. To illustrate where and how these changes occur, we then construct a bifurcation diagram for a simple family of dynamic equations. However, these results are only true if we can move continuously through our domains, i.e, the time scales. In the last part of this thesis, we define what it means to have a convergent sequence of time scales. Then we use this definition to prove that the limit …