A fractional order HBV model with hospitalization

Abstract

Hepatitis B is a viral infection that can cause both acute and chronic disease and mainly attacks the liver. The present paper describes the dynamics of HBV with hospitalization. Due to the fatal nature of this disease, it is necessary to formulate a new mathematical model in order to reduce the burden of HBV. Therefore, we formulate a new HBV model with fractional order derivative. The fractional order model is formulated in Caputo sense. Two equilibria for the model exist: the disease-free and the endemic equilibriums. It is shown, that the disease-free equilibrium is both locally and globally asymptotically stable if \begin{document}$ \mathcal{R}_0 for any \begin{document}$ \alpha\in(0,1) $\end{document} . The sensitivity analysis of the model parameters are calculated and their results are depicted. The numerical results for the stability of the endemic equilibrium are presented. The complex dynamics of the disease can be best described by using the fractional derivative and this is illustrated through many graphical results.