A generalized fractional hepatitis B virus infection model with both cell-to-cell and virus-to-cell transmissions.

In this paper, we suggest a generalized fractional hepatitis B viral infection model with two modes of transmission that are cell-to-cell and virus-to-cell. These two modes of transmission will be represented by two generalized incidence functions. We take into account the human body's adaptive immunity, which is represented by antibody and cytotoxic T-lymphocyte immune responses. We begin the study of this model by giving some theorems concerning the existence, positivity and boundness of the model solutions. We have shown that the model has a free-disease equilibrium point and other four endemic steady states. We give the relationship between the existence of these steady states and their corresponding reproductive numbers. By using the Lyapunov method and LaSalle's invariance principle, we have shown the different theorems concerning the global stability of steady states. Some numerical simulations are presented to confirm our theoretical findings about the stability of steady states and to show the effectiveness of fractional derivative order on the stability of all equilibria. We observe that the choice of generalized incidence functions can provide a clearer understanding of the stability of equilibria and can incorporate a wide range of classical incidence functions. Finally, good infection treatment helps considerably to irradiate the infection. [ABSTRACT FROM AUTHOR]