A study on fractional-order lung cancer model under different internal influences with time delays analysis and modeling

This paper proposes a sophisticated mathematical model for the dynamics of lung cancer, involving Caputo-type fractional derivatives and interaction-specific time delays. The model characterizes the populations of lung epithelial cells, immune cells, and mutated cells, elucidating their nonlinear interactions and external influences. Fractional derivatives introduce memory effects, while time delays capture the biological latency in cellular interactions. This refined approach allows a deeper understanding of lung cancer progression and offers a robust framework to investigate therapeutic strategies. Hyers-Ulam stability and delay sensitivity were performed alongside other analytic computations. An advanced numerical analysis using the Adams-Bashforth-Moulton method was used to simulate the model. The model demonstrates the competitive balance between cellular growth and decay, which are interdependent and serve as the basis for further applications in cancer studies. The results show that the delays account for the latency of the immune response and the time required for cellular interactions, leading to a reduced growth rate compared to the basic reproduction number. These new perspectives highlight areas and directions to improve medical interventions.