A generalized fractional hepatitis B virus infection modelwith both cell-to-cell and virus-to-cell transmissions

Abstract

In this paper, we suggest a generalized fractional hepatitis B viral infection model with twomodes of transmission that are cell-to-cell and virus-to-cell. These two modes of transmissionwill be represented by two generalized incidence functions. We take into account the humanbody adaptive immunity, that is represented by antibody and cytotoxic T-lymphocyte immuneresponses. 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 betweenthe existence of these steady states and their corresponding reproductive numbers. By usingthe Lyapunov method and LaSalle's invariance principle, we have shown the different theoremsof global stability to the problem steady states. Some numerical simulations are presented inorder to confirm our theoretical fndings about the stability of steady states and to show the effectiveness of fractional derivative order on the stability of all equilibria. We observe that thechoice 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 infectiontreatment helps considerably to irradiate the infection.