Adaptive boundary layer double integral sliding mode controller design for leukemia therapy

Presence of leukocytes in huge amount in the bone marrow and blood causes blood cancer or leukemia. In leukemia, number of white blood corpuscles in blood increases rapidly. Chemotherapy treatment is the most useful treatment of leukemia. Although chemotherapy treatment can reduce the cancer cells effectively, it destroys the healthy cells of the body as well. Therefore, it is essential to develop a proper control structure to use the chemotherapy agent effectively to reduce the cancer cells and to keep the normal cells within specified limit. An adaptive boundary layer double integral sliding mode controller is designed in this article for treatment of acute leukemia using chemotherapy. The objective of the designed controller is to control the chemotherapy agent in such a way that the amount of leukemic cell become zero and at the same time, the number of healthy cells should be retained at a desired level. The stability of the designed controller is verified using a Lyapunov function. The consequences of chemotherapy treatment on both natural cells and cancer cell using the designed controller is observed in both monotonic and non-monotonic therapy function. A comparative analysis is also carried out between the designed controller and some existing controller to verify the effectiveness of the proposed controller.