Stochastic Optimization Models for Cancer Chemotherapy

Abstract

Aims: The study is conducted with the objective of deriving the growth and loss rates of cancer causing cells by formulating two optimization problems based on Two Stage Stochastic Model for Cancer Cell growth developed by Srinivasa Rao and Tirupathi Rao [10]. It has significant usage in development of decision support systems for optimal drug administration by health care industry for cancer chemotherapy protocols. Study Design: The study is designed for developing the optimization programming problems with two different aims. The primary one is to minimize the expected intensity of cancer causing cells either in mutant or malignant stage, the other is to minimize the stay time of cancer causing cell in the tumor. The subjective constraints are designed with maximum expected levels and limits on variability size of cancer causing cells in mutant and malignant stages. The constraints of the other problem are the expected durations of cancer causing cell in mutant stage, in malignant stage, from mutant stage to malignant stage should not exceed to some targeted time; and the other constraint is on the maximum limit on the variability size of the tumor duration should not be more than some specified limit. Methodology: The study is further analyzed with the simulated numerical illustrations. The optimization results on the decision parameters were explored and the interpretations were made accordingly. The basic methodology is divided in to two parts. In part-1 the formulation of programming problems was carried out through theoretical notion of Stochastic programming. In part-2 the decision variables were obtained through the numerical illustrations. Interpretations on the cancer chemotherapy and effectiveness of treatment are arrived.