Stochastic Modeling & Optimization Methods. Studies on Cancer Growth and Control

      Аннотация: This book has discussed some stochastic models on cancer cell growth with Bi-variate stochastic processes. The pathophysiology of cancer growth was modeled with postulates of Poisson processes. In the first phase, the mathematical relations for various statistical measures like expected number, variances of both normal and mutant cells were derived for normal and mutant cells. The second phase deals with extension of proposed model to study the tumor behaviour during drug administration and during drug vacation as a part of cancer treatment with chemotherapy. Sensitivity analysis of the model is carried out with suitable simulated numerical data. Stochastic model for cancer growth as a result of spontaneous mutation and proliferation of cells during drug vacation and during chemotherapy were developed. The model is extended for two stage mutant cell growth. The third phase of the study has formulated two stochastic programming problems for optimal drug administration in drug presence and absence, for calculating the drug effectiveness during chemotherapy. Health care industry may make use of these studies for optimal management of disease

Ключевые слова: Optimal Drug Administration, Cancer Chemotherapy, Stochastic Modeling of Cancer Growth, Stochastic Optimizations Programming, Bi-variate Poisson Processes