Some Control Policies for Control of Cancer

Abstract

To control cancer, a patient goes through different treatment procedures such as surgery, drug therapy, radiotherapy and also sometimes integrated control of two or more therapy simultaneously. The treatment procedure depends solely upon the stage of cancer at the time of diagnosis. So the mathematical modeling of cancer under different control policy is very complex in nature. In this paper, an attempt has been made to formulate control policies to control cancer under drug therapy in the form of chemotherapy. The drug administered to a patient is assumed to be time dependent variable and primary assumption is that the drug kills both tumor and immune cells. The rate of drug administration at time t assumes to follow three different mathematical models such as (a) Exponential (b) logistic and (c) Oscillatory. The control variable 𝑣(𝑡) represents the drug administered at time t. Immune -Tumor cell growth are subjected to these drug models as mentioned above and the behavior of Tumor growth has been numerically analyzed A comparison on the behavior of tumor cell growth under these drug model give rise to a significant result and conclusion.