title: Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of BCG treatment of bladder cancer.
abstract: Understanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed by Bunimovich-Mendrazitsky et al., who explored the immune response in bladder cancer as an effect of BCG treatment. This treatment exploits the host's own immune system to boost a response that will enable the host to rid itself of the tumor. Although this model was extensively studied using numerical simulation, no analytical results on global tumor dynamics were originally presented. In this work, we analyze stability in a mathematical model for BCG treatment of bladder cancer based on the use of quasi-normal form and stability theory. These tools are employed in the critical cases, especially when analysis of the linearized system is insufficient. Our goal is to gain a deeper insight into the BCG treatment of bladder cancer, which is based on a mathematical model and biological considerations, and thereby to bring us one step closer to the design of a relevant clinical protocol.
authors.affiliation: Ariel University Center of Samaria, Mathematics Department, Ariel, Israel. SvetlanaBu@ariel.ac.il
authors.forename: Svetlana
authors.initials: S
authors.lastname: Bunimovich-Mendrazitsky
authors.forename: Yakov
authors.initials: Y
authors.lastname: Goltser
mesh_terms: D000818:Animals; D001500:BCG Vaccine / Q000008:administration & dosage* / Q000276:immunology*; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D004360:Drug Therapy, Computer-Assisted / Q000379:methods*; D006801:Humans; D008954:Models, Biological; D016896:Treatment Outcome; D001749:Urinary Bladder Neoplasms / Q000188:drug therapy* / Q000276:immunology*
chemical_list: D001500:BCG Vaccine