An optimization method for treating solid tumors with combined therapy using the great deluge algorithm

. In this work, we implement an optimization technique on a previously developed mathematical model for malignant pleural mesothelioma. The goal is to optimize a dynamical system that models the tumor microenvironment as an ecosystem involving host, immune, tumor and endothelial cells. The objective functional used in our analysis minimizes the accumulation of the cancer cell population and the toxic effects of a combination of chemotherapy and anti-angiogenic therapy. We use the great deluge algorithm to solve an optimization problem in which the optimal times to administer each therapy are determined over the course of a 250 day treatment period. We also consider three distinct scenarios regarding the effect of chemotherapy on the immune response: stimulatory, neutral, and inhibitory. Our results demonstrate that the immune system, particularly the effect of chemotherapy on the immune system, plays a critical role in achieving tumor elimination.