Stability analysis of a fractional-order novel hepatitis B virus model with immune delay based on Caputo-Fabrizio derivative. (January 2021)

• Record Type: Journal Article
• Authors: Gao, Fei; Li, Xiling; Li, Wenqin; Zhou, Xianjin
• Is Part Of: Chaos, solitons and fractals. Volume 142(2021)
• Publication Date: 2021-01
• Subjects: Caputo-Fabrizio derivative -- fractional order -- HBV -- immune delay -- stability; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110436
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Considering different populations (cells and viruses) and using different fractional orders compared to the primary hepatitis B virus model. Considering the dimensional consistency to avoid this dimensional mismatching in the Caputo-Fabrizio derivative model. In addition to the existence and uniqueness, the positivity and boundedness of the solution are also proved. Using the stability theory of fractional order system, the stability and bifurcation of equilibrium point are discussed. The numerical simulation with the predictor-corrector Adams Bashforth-Moulton (ABM) technique is used to draw the dynamic diagram of the model for different fractional order parameter values, and different numerical results are obtained. Abstract: In mathematical epidemiology, mathematical models play a vital role in understanding the dynamics of infectious diseases. Therefore, in this paper, a novel mathematical model for the hepatitis B virus (HBV) based on the Caputo-Fabrizio fractional derivative with immune delay is introduced, while taking care of the dimensional consistency of the proposed model. Initially, the existence and uniqueness of the model solutions are proved by Laplace transform and the fixed point theorem. The positivity and boundedness of the solutions are also discussed. Sumudu transform and Picard iteration were used to analyze the stability and iterative solution of the fractional order model of HBV. Further, using the stability theory of fractional order system, the stability and bifurcation of equilibrium point are discussed. Finally, results are presented for different values of the fractional parameter.