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

Abstract

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.