Mathematical modeling of combined therapies for treating tumor drug resistance.

Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried out to verify the stability of equilibria and treatment outcomes using a set of collected model parameters and experimental data on murine colon carcinoma. Simulation results suggest that immunotherapy combined with chemotherapy contributes significantly to the control of tumor growth compared to monotherapy. Sensitivity analysis is performed to identify the importance of model parameters on the variations of model outcomes.