Adaptive Short Term Ahead Tumor Growth Inhibition Prediction Subjected in Anticancer Agents Given in Combination Combination chemotherapy, i.e. multiple anticancer drugs given in combination, is a very common strategy combating cancer. Despite the high complexity of the disease, the tumor and drug dynamics and kinetics can be mathematically described and modeled and numerically simulated accurately enough. In this article, the development and parameter identification of a dynamic inputoutput statespace mathematical model capable of simulating with accuracy the tumor growth in xenografted mice under the effects of antineoplastic drug agents in combination is first carried out. Through a nonlinear optimization algorithm and Monte Carlo simulations the pharmacodynamicpharmacokinetic (PKPD) parameters values of the dynamic inputoutput mathematical model were estimated for specific cases of drugs administered in combination, with the objective the mathematical model to best fit in the experimental data. Then, the ability of the identified nonlinear tumor growth inhibition (TGIadd) statespace model to forecast with precision in the shortterm i.e. one, two or three steps ahead in the near future the tumor growth under the effects of anticancer agents administered in combination was explored and through the same two numerical experiments was evaluated and confirmed. It is shown that such a high prediction power of the specific tumor growth inhibition mathematical model is of great importance at a clinical context, since it could provide oncologists an important help in the appropriate modification of a combination chemotherapy strategy to optimize it and make it more personalized and consequently more effective, thus prolonging patientu0027s life.

A dual approach for positive Txe2x80x93S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy Abstract   This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and immunexe2x80x93competent cells from the malignant region into the region of benign growth where the immune system can inhibit tumor growth. In order to achieve this goal, a new modeling strategy is used that is based on Takagixe2x80x93Sugeno. A TakagiSugeno fuzzy model is derived based on the Stepanova nonlinear model that enables a systematic design of the controller. Then, a positive Parallel Distributed Compensation controller is proposed based on a linear copositive Lyapunov Function so that the tumor volume and administration of the chemotherapeutic and immunotherapeutic drugs is reduced, while the density of the immunecompetent cells is reached to an acceptable level. Thanks to the proposed strategy, the entire control design is formulated as a Linear Programming problem. Finally, the simulation results show the effectiveness of the proposed control approach for the cancer treatment.