Dynamics analysis and optimal control of a fractional-order lung cancer model

This study presented a novel Caputo fractional-order lung cancer model aimed at analyzing the population dynamics of cancer cells under untreated conditions and different treatment strategies. First, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the stability of the tumor-free equilibrium state and the internal equilibrium state. Second, we explored the existence, uniqueness, and positivity of the model's solutions and analyzed the stability of the tumor-free equilibrium state and the internal equilibrium state. We calculated the basic reproduction number and conducted a sensitivity analysis to evaluate the impact of various parameters on cancer cell growth. Next, by considering surgery and immunotherapy as control measures, we discussed the existence of an optimal solution and derived its expression using the Pontryagin maximum principle. We then performed numerical simulations of limit cycles, chaos, and bifurcation phenomena under uncontrolled conditions, as well as the dynamic behavior of cells under different control strategies. Finally, using real data from lung cancer patients, we conducted parameter estimation and curve fitting through the least squares method. The results indicated that combined therapy showed better effectiveness in inhibiting tumor cell growth, significantly outperforming single treatment strategies and more effectively controlling the progression of cancer.