A mixed radiotherapy and chemotherapy model for treatment of cancer with metastasis

In this paper, a mathematical model of cancer treatment, in the form of a system of ordinary differential equations, by chemotherapy and radiotherapy where there is metastasis from a primary to a secondary site has been proposed and analyzed. The interaction between immune cells and cancer cells has been examined, and the chemotherapy agent has been considered as a predator on both normal and cancer cells. The metastasis may be time delayed. For better investigation of the treatment process and based on physical investigation, the immanent effects of inputs on cancer dynamic have been investigated. It is supposed that the interaction between NK cells and tumor cells changes during the chemotherapy. This novel approach is useful not only to gain a broad understanding of the specific system dynamics but also to guide the development of combination therapies. The analysis is carried out both analytically (where possible) and numerically. By considering such immanent effects, the tumor‐free equilibrium point will be stable at the end of treatment, and the tumor can not recur again, and the patient will totally recover. So, the present analysis suggests that a proper treatment method should change the dynamics of the cancer instead of only reducing the population of cancer cells. Copyright © 2016 John Wiley & Sons, Ltd.