Homotopy decomposition method to analysis fractional hepatitis B virus infection model

Abstract

Mathematical models have been employed to investigate the factors that govern the progression of infectious diseases in viral infections. This article investigates a fractionalised model for hepatitis B virus infection, curing infected cells. We analysed the fractional hepatitis B virus infection model using the homotopy decomposition method (HDM). Additionally, the existence and uniqueness of the fractional model are considered. The graphical solutions depicted that when introducing a fractional-order derivative to the model, the peak of viral propagation is reduced, and cell damage is minimised by initiating treatment at an early stage; however, the disease takes a longer time to be eradicated. The outcomes may also be valuable in the fields of clinical science and medicine. This model provided insights into the natural history of HBV infection, including the different stages of infection (acute, chronic, and resolved) and the likelihood of progression from one stage to another. This information is essential for predicting disease outcomes and planning appropriate clinical management for patients.

Keywords

• hbv infection model
• riemann–liouville fractional derivative
• homotopy decomposition technique
• fixed point theorem