Analysis of Tumor‐Immune Dynamics With T Cells and Dendritic Cells Using Fractional Extension of He‐Laplace Framework

ABSTRACT

Computational modeling provides a useful framework for investigating cancer‐immune dynamics and the interactions between tumor cells and immune components. In this study, a nonlinear fractional cancer‐immune model incorporating CD4+ T cells, CD8+ T cells, dendritic cells, IL‐2, IL‐12, and anti‐PD‐L1 inhibitors is investigated in the Caputo sense. The proposed system is solved using the He‐Laplace algorithm to obtain approximate series solutions for the seven coupled state variables. The accuracy of the obtained solutions is assessed through residual‐error analysis, and the corresponding results are presented in tabulated form. Two‐dimensional, three‐dimensional, and contour plots are further employed to examine the effects of the model parameters and fractional order on the system dynamics. The results indicate that the considered immune and therapeutic components produce noticeable changes in tumor and immune‐cell profiles, while variations in the fractional parameter influence the obtained solutions. The study provides a theoretical computational framework for analyzing complex fractional cancer‐immune dynamics and the interactions among the incorporated biological components.