A novel investigation of the hepatitis B virus using a fractional operator with a non-local kernel

In order to understand and manage infectious illnesses, mathematical models are extremely important. They support decision making by researchers and public health workers in predicting the spread of diseases, evaluate the results of interventions, and gathering data. This study considers a fractionalized hepatitis B virus (HBV) infection model with cell cure. The Atangana Baleanu fractional model was initially established for the epidemic issue. This paper analyses the fractional form that makes up the HBV infection model utilizing the numerical methodology, homotopy analysis transform method (HATM). The suggested technique is created with the use of the homotopy analysis method (HAM), the homotopy polynomial, and the Laplace transformation. Additionally, the existence and uniqueness of the solution are considered, and stability analysis is given by the fixed-point theory (FPT) of the HBV model. Through MATLAB21, the obtained solutions are graphically simulated. The graphical solutions demonstrated that the peak of viral propagation is reduced when a fractional-order derivative is included to the model, and cell damage is minimized by starting treatment early on; however, the disease takes longer to be completely eradicated. The outcomes will be beneficial in the medical field. The fractional model lets us draw significant information essential for predicting disease outcomes and planning appropriate clinical management for patients.