Using Pontryagin’s Minimum Principle for Optimal Control of Chemotherapy on a Cancerous Tumour

Obesity and high caloric diet as dangerous factors have sufficient rolls in different types of cancers such as breast cancer and colorectal cancer among others. In this work we use a mathematical model of cancer tumour growth that takes into account the immune system response and will study the effects of obesity on the organism with cancer. The progress of a cancer tumour is a complex biological process that involves the interaction of different cell populations. The model consists of four ordinary differential equations with a logistic equation for the growth of the amount of fat stored. The optimal control solution by regarding to the pontryagin’s Minimum principle which is an important principle in optimal theory, is used as the Innovation of this study and the main interest is to provide insights about the qualitative and quantitative possible effects of a low/high caloric diet on the chemotherapy protocols when different immune system responses are considered. We summarized the parameters of our mathematical model which may vary from case to case. According to our model the immune system response and the diet are important factors and their interaction could lead to improved chemotherapy protocols

کلیدواژه ها:

Cancer ، Chemotherapy ، Obesity ، Optimal Control ، Pontryagin’s Min principle