Hernandez, Jason2010-12-232010-12-232010http://udspace.udel.edu/handle/19716/5732We have developed a multi-state ordinary differential equation model representing the dynamics of cancerous cell populations under conditions consistent with the gene therapy technique proposed by Martinez-Quintanilla et al. The model is based on a variation of the Lotka-Volterra equations, a method to illustrate multiple species’ competition to utilize a scarce resource. This system allows for investigation of the effectiveness of proposed anti-cancer gene therapy methods, including the response to selective pressures resulting from drug treatments. In this thesis, we observe the stability of the system via bifurcation analysis; highlight the importance of delivery method of drug-susceptibility genes; finally, propose a control method to optimize treatment effectiveness.Cancer -- Gene therapyEvolution (Biology)Drug resistanceThesis