| Summary: | A fractional model for the transmission dynamics of Hepatitis B was designed. Hepatitis B disease has a great impact on global human health conditions and economical systems. The spreading of HBV disease has several phases, i.e., acute and chronicle carriers phases have a key role. The chronicle carrier’s cases do not have any signs and are capable of transmitting the Hepatitis B infection. In this article, we investigated the transmission due to different infection phases of the Hepatitis B virus and constructed a nonlinear epidemic. Next, a fractional hepatitis B virus model with Atangana–Baleanu derivative (AB derivative) is formulated with vaccine effects. Firstly, we calculated the basic reproductive value and equilibria of the proposed model. Qualitative analysis of the approximate root of the said problem has been derived with the help of Fixed Point Theory. The Iterative approximate technique with the help of the Adams–Bashforth predictor–corrector scheme for evaluating the considered fractional system having the ABC derivative is expressed. In the last, a graphical representation is established to show the obtained scheme findings and compare different non-integer orders of Ψ.
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