ADVANCED DYNAMIC NUMERICAL SCHEME FOR FRACTAL-FRACTIONAL DIFFERENTIAL OPERATORS FOR CYTOTOXIC T LYMPHOCYTE MODEL PERTAINING TO MITTAG-LEFFLER KERNEL

In this paper, a virus mechanism framework involving cytotoxic T lymphocyte (CTL) and antibody immunologic reactions is developed and tested by using the fractal-fractional scheme in the Atangana–Baleanu viewpoint. The framework takes into account two types of viral particles: chronically diseased cells and assertively contaminated cells that generate pathogens. The system represents both virus-to-cell (V-C) and cell-to-cell (C-C) prorogation. According to the framework, the emergence of persistent viruses is primarily supplemented by an enduring antibody reaction, whereas CTLs are not kept at significant concentrations. To ensure the biological viability of the suggested approach, we demonstrate the positivity and boundedness of the system’s strategies. Besides that, Lyapunov mechanisms were applied in the study to examine whether the model’s equilibria are globally asymptotically rigorous. The fractal-fractional Atangana–Baleanu operator in the Caputo viewpoint is employed to design the roles of CTLs and antibody responses, which is a revolutionary procedure that was implemented to demonstrate its mathematical comprehension of C-C infestation and elevate the number of virus particles, whereas the humoral immunological system efficaciously neutralizes pathogen intensity and has a less significant impact on pathogen reduction. Moreover, we provided the numerical techniques for estimating the system’s solutions using the Adams-Bashforth procedure and the Newton polynomials approach. We visualize and compare our outcomes using the aforesaid schemes. When using the Newton polynomial, the numerical findings demonstrate certain stability and a dearth of noticeable order in the initial phases of disease complexities.