TY - JOUR A2 - Galdi, Giovanni P. AU - Sharma, Swarnali AU - Samanta, G. P. PY - 2013 DA - 2013/07/14 TI - Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control SP - 608598 VL - 2013 AB - We have considered a tumor growth model with the effect of tumor-immune interaction and chemotherapeutic drug. We have considered two immunecomponents—helper (resting) T-cells which stimulate CTLs and convert them intoactive (hunting) CTL cells and active (hunting) CTL cells which attack, destroy, oringest the tumor cells. In our model there are four compartments, namely, tumorcells, active CTL cells, helper T-cells, and chemotherapeutic drug. We have discussed the behaviour of the solutions of our system. The dynamical behaviour of oursystem by analyzing the existence and stability of the system at various equilibriumpoints is discussed elaborately. We have set up an optimal control problem relativeto the model so as to minimize the number of tumor cells and the chemotherapeutic drug administration. Here we used a quadratic control to quantify this goaland have considered the administration of chemotherapy drug as control to reducethe spread of the disease. The important mathematical findings for the dynamicalbehaviour of the tumor-immune model with control are also numerically verifiedusing MATLAB. Finally, epidemiological implications of our analytical findings areaddressed critically. SN - 2356-7503 UR - https://doi.org/10.1155/2013/608598 DO - 10.1155/2013/608598 JF - Journal of Nonlinear Dynamics PB - Hindawi Publishing Corporation KW - ER -