A new Hepatitis B model in light of asymptomatic carriers and vaccination study through Atangana–Baleanu derivative
LI Xiao-ping, Nadia Gul, Muhammad Altaf Khan, Rubi Bilal, Aatif Ali, Mohammad Y. Alshahrani, Taseer Muhammad, Saeed Islam
Abstract
We formulate a new mathematical model for better understanding of the dynamics of Hepatitis B virus (HBV) with asymptomatic carriers and vaccination classes. Initially, we first formulate the problem in integer order derivative and then apply the fractional operator to extend the model due to advantages of the he fractional derivative. We carefully examine the local and global asymptotical analysis of the model in integer order. We found when R0<1, then the model is locally as well as globally asymptotically stable. The fractional order model and its existence and uniqueness are derived. In order to analyze the model solution of the fractional order graphically, we carried out more detailed numerical results for the parameters that have a great effect on the disease eliminations through a useful numerical approach using the Mittag-Leffler approach.