A NEW MATHEMATICAL MODELING AND SUB-OPTIMAL CHEMOTHERAPY OF CANCER

Abstract

The development of more accurate cancer mathematical models leads to present more realistic treatment protocols, especially in model-based treatment protocol design. Hence, a cancer mathematical model is presented by considering tumor cells, immune cells, interleukins, macrophages polarization, and chemotherapy based on biological concepts. Both local and global sensitivity analyses are done to examine the effect of changing the parameters on the final tumor population. Then, the tumor-free equilibrium points of the system are derived, and their stabilities are studied. The main target of chemotherapy is to eliminate the tumor while limiting drug toxicity. The SDRE method is used to construct a sub-optimal control strategy by using the developed nonlinear cancer model. For simulation, three patients are considered: a young patient, an old patient, and a pregnant patient. These cases have different immune system strengths. Also, three initial tumor sizes are regarded for each case. So, different treatment strategies are suggested. Eradication of tumor cells in a finite duration with a desired amount of chemo-drug is shown in the simulation results. The results confirmed that the immune system’s ability plays an important role in treatment success. It is shown that there are different treatment protocols for different patients, and the SDRE method is more flexible and effective than the others.