Mathematical models and dynamic behaviors of cancer treatment by continuous and pulsed radiotherapy

Abstract

In this study, two mathematical models are introduced to describe treatment of cancer by continuous and pulsed radiotherapy. In the continuous radiotherapy model, we determine all of the equilibrium points and conduct a thorough examination of the stability of these equilibria. Criterions of the radiation dose that guarantee the cancer to be eradicated or take a positive balance with normal cells are provided. In the pulsed radiotherapy model, conditions of the existence and stability of cancer win periodic solution, cancer eradication periodic solution and coexistent periodic solution are derived. Meanwhile, numerical simulations to the effect of radiation dose on the cure and spread of the cancer are carried out. A brief conclusion is presented, as well as a few intriguing subjects for additional investigation are discussed.