A numerical study of a mathematical model of pulsed immunotherapy for superficial bladder cancer

摘要

Intravesical BacillusCalmette-Guérin (BCG) is a treatment for superficial bladder cancer. A mathematical model of pulsed BCG immunotherapy for superficial bladder cancer is considered. The mathematical model using impulsive differential equations is turned into a discrete-time dynamical system for bifurcation analysis. A numerical method is then proposed for identifying the fixed points and the bifurcations of the fixed points. One-parameter bifurcation diagrams are computed for showing fixed-point curves. Bistability exists in the model. Both tumor-free and high-tumor states are stable in a parameter range. The minimum dosage for successful treatment which depends on the initial tumor size and individual patient is determined. Two-parameter bifurcation diagrams are computed. The parameter domain is divided into regions for failure treatment, successful treatment of a tumor with a restricted initial size, and treatment with side-effect occurrence. It is believed that the numerical method proposed in this paper can be applied to a class of mathematical models of periodically pulsed drug therapies.