Modeling and numerical analysis of fractional order hepatitis B virus model with harmonic mean type incidence rate
Rahat Zarin
Abstract
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 (ABC) operator with vaccination effects. The threshold number R0 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 ABC 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.