Dynamical Analysis of Microbiome-Based Tumor Therapeutics Using a Fractional Derivative Approach

This work investigates a novel fractional-order tumor growth model. The model explores the complex interactions among tumor cells, the immune system, and the microbiome. The Atangana-Baleanu fractional operator, which effectively captures memory and hereditary properties occurring in biological systems, has been used in model formulation. An efficient numerical approach based on the Adam-Bashforth method and predictor-corrector scheme is applied to the model’s solution. Stability and convergence have been demonstrated through numerical simulations. Furthermore, it has been shown graphically that changes in microbiome composition and immune response inuence tumor growth across various fractional orders. The results highlight the significance of microbiome dynamics and fractional calculus in cancer modeling.