Al Qurashi, MaysaaRashid, SaimaJarad, FahdMatematik2024-02-092024-02-092022Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd. (2022). "A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay", Mathematical Biosciences and Engineering, Vol.19, No.12, pp.12950-12980.1551-0018https://doi.org/10.3934/mbe.2022605Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.eninfo:eu-repo/semantics/openAccessHbv ModelFractal-Fractional Caputo-Fabrizio Di Fferential OperatorsExistence And UniquenessQualitative AnalysisNumerical SolutionArticle1912129501298010.3934/mbe.20226052-s2.0-85138662534WOS:00086241160002136654030Q2Q2