Modeling and numerical analysis of fractional order hepatitis B virus model with harmonic mean type incidence rate.

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A mathematical epidemiological model for the transmission of Hepatitis B virus in the frame of fractional derivative with harmonic mean type incidence rate is proposed in this article. The proposed mathematical model is then fictionalized by utilizing the Atangana-Baleanu-Capotu ( A B C ) operator with vaccination effects. The threshold number R 0 is calculated by utilizing the next-generation matrix approach. The existence and uniqueness of solution of the proposed model are proved by utilizing the well-known fixed point theory. For the numerical solution of the proposed model with A B C derivative the well-known Adams-Bashforth-Molton (ABM) method is utilized. Likewise, stability is required in regard of the numerical arrangement. In this manner, Ulam-Hyers stability utilizing nonlinear functional analysis is utilized for the proposed model.